sint<-√3/2 inequation

Given the inequality:
$$\sin{\left(t \right)} < \frac{\left(-1\right) \sqrt{3}}{2}$$
To solve this inequality, we must first solve the corresponding equation:
$$\sin{\left(t \right)} = \frac{\left(-1\right) \sqrt{3}}{2}$$
Solve:
$$x_{1} = -19.8967534727354$$
$$x_{2} = 24.0855436775217$$
$$x_{3} = -101.57816246607$$
$$x_{4} = -95.2949771588904$$
$$x_{5} = -89.0117918517108$$
$$x_{6} = -2.0943951023932$$
$$x_{7} = 49.2182849062401$$
$$x_{8} = -14.6607657167524$$
$$x_{9} = 86.9173967493176$$
$$x_{10} = -45.0294947014537$$
$$x_{11} = 54.4542726622231$$
$$x_{12} = -46.0766922526503$$
$$x_{13} = -63.8790506229925$$
$$x_{14} = -8.37758040957278$$
$$x_{15} = -32.4631240870945$$
$$x_{16} = -114.144533080429$$
$$x_{17} = 5.23598775598299$$
$$x_{18} = -83.7758040957278$$
$$x_{19} = 60.7374579694027$$
$$x_{20} = -71.2094334813686$$
$$x_{21} = -76.4454212373516$$
$$x_{22} = 23.0383461263252$$
$$x_{23} = 74.3510261349584$$
$$x_{24} = 16.7551608191456$$
$$x_{25} = 10.471975511966$$
$$x_{26} = -38.7463093942741$$
$$x_{27} = 42.9350995990605$$
$$x_{28} = -70.162235930172$$
$$x_{29} = -7.33038285837618$$
$$x_{30} = 68.0678408277789$$
$$x_{31} = -64.9262481741891$$
$$x_{32} = -51.3126800086333$$
$$x_{33} = -58.6430628670095$$
$$x_{34} = 29.3215314335047$$
$$x_{35} = 55.5014702134197$$
$$x_{36} = -27.2271363311115$$
$$x_{37} = 93.2005820564972$$
$$x_{38} = -33.5103216382911$$
$$x_{39} = 30.3687289847013$$
$$x_{40} = -151.843644923507$$
$$x_{41} = 11.5191730631626$$
$$x_{42} = 4.18879020478639$$
$$x_{43} = -90.0589894029074$$
$$x_{44} = -13.6135681655558$$
$$x_{45} = -20.943951023932$$
$$x_{46} = 36.6519142918809$$
$$x_{47} = -11851.1346868919$$
$$x_{48} = -1559.27715373173$$
$$x_{49} = 79.5870138909414$$
$$x_{50} = 61.7846555205993$$
$$x_{51} = 73.3038285837618$$
$$x_{52} = -26.1799387799149$$
$$x_{53} = 85.870199198121$$
$$x_{54} = -82.7286065445312$$
$$x_{55} = 98.4365698124802$$
$$x_{56} = -5606.69568910658$$
$$x_{57} = -77.4926187885482$$
$$x_{58} = 48.1710873550435$$
$$x_{59} = 41.8879020478639$$
$$x_{60} = -57.5958653158129$$
$$x_{61} = 393.746279249921$$
$$x_{62} = 35.6047167406843$$
$$x_{63} = 17.8023583703422$$
$$x_{64} = -1.0471975511966$$
$$x_{65} = 99.4837673636768$$
$$x_{66} = -96.342174710087$$
$$x_{67} = 92.1533845053006$$
$$x_{68} = 67.0206432765823$$
$$x_{69} = 80.634211442138$$
$$x_{70} = -52.3598775598299$$
$$x_{71} = -39.7935069454707$$
$$x_{1} = -19.8967534727354$$
$$x_{2} = 24.0855436775217$$
$$x_{3} = -101.57816246607$$
$$x_{4} = -95.2949771588904$$
$$x_{5} = -89.0117918517108$$
$$x_{6} = -2.0943951023932$$
$$x_{7} = 49.2182849062401$$
$$x_{8} = -14.6607657167524$$
$$x_{9} = 86.9173967493176$$
$$x_{10} = -45.0294947014537$$
$$x_{11} = 54.4542726622231$$
$$x_{12} = -46.0766922526503$$
$$x_{13} = -63.8790506229925$$
$$x_{14} = -8.37758040957278$$
$$x_{15} = -32.4631240870945$$
$$x_{16} = -114.144533080429$$
$$x_{17} = 5.23598775598299$$
$$x_{18} = -83.7758040957278$$
$$x_{19} = 60.7374579694027$$
$$x_{20} = -71.2094334813686$$
$$x_{21} = -76.4454212373516$$
$$x_{22} = 23.0383461263252$$
$$x_{23} = 74.3510261349584$$
$$x_{24} = 16.7551608191456$$
$$x_{25} = 10.471975511966$$
$$x_{26} = -38.7463093942741$$
$$x_{27} = 42.9350995990605$$
$$x_{28} = -70.162235930172$$
$$x_{29} = -7.33038285837618$$
$$x_{30} = 68.0678408277789$$
$$x_{31} = -64.9262481741891$$
$$x_{32} = -51.3126800086333$$
$$x_{33} = -58.6430628670095$$
$$x_{34} = 29.3215314335047$$
$$x_{35} = 55.5014702134197$$
$$x_{36} = -27.2271363311115$$
$$x_{37} = 93.2005820564972$$
$$x_{38} = -33.5103216382911$$
$$x_{39} = 30.3687289847013$$
$$x_{40} = -151.843644923507$$
$$x_{41} = 11.5191730631626$$
$$x_{42} = 4.18879020478639$$
$$x_{43} = -90.0589894029074$$
$$x_{44} = -13.6135681655558$$
$$x_{45} = -20.943951023932$$
$$x_{46} = 36.6519142918809$$
$$x_{47} = -11851.1346868919$$
$$x_{48} = -1559.27715373173$$
$$x_{49} = 79.5870138909414$$
$$x_{50} = 61.7846555205993$$
$$x_{51} = 73.3038285837618$$
$$x_{52} = -26.1799387799149$$
$$x_{53} = 85.870199198121$$
$$x_{54} = -82.7286065445312$$
$$x_{55} = 98.4365698124802$$
$$x_{56} = -5606.69568910658$$
$$x_{57} = -77.4926187885482$$
$$x_{58} = 48.1710873550435$$
$$x_{59} = 41.8879020478639$$
$$x_{60} = -57.5958653158129$$
$$x_{61} = 393.746279249921$$
$$x_{62} = 35.6047167406843$$
$$x_{63} = 17.8023583703422$$
$$x_{64} = -1.0471975511966$$
$$x_{65} = 99.4837673636768$$
$$x_{66} = -96.342174710087$$
$$x_{67} = 92.1533845053006$$
$$x_{68} = 67.0206432765823$$
$$x_{69} = 80.634211442138$$
$$x_{70} = -52.3598775598299$$
$$x_{71} = -39.7935069454707$$
This roots
$$x_{47} = -11851.1346868919$$
$$x_{56} = -5606.69568910658$$
$$x_{48} = -1559.27715373173$$
$$x_{40} = -151.843644923507$$
$$x_{16} = -114.144533080429$$
$$x_{3} = -101.57816246607$$
$$x_{66} = -96.342174710087$$
$$x_{4} = -95.2949771588904$$
$$x_{43} = -90.0589894029074$$
$$x_{5} = -89.0117918517108$$
$$x_{18} = -83.7758040957278$$
$$x_{54} = -82.7286065445312$$
$$x_{57} = -77.4926187885482$$
$$x_{21} = -76.4454212373516$$
$$x_{20} = -71.2094334813686$$
$$x_{28} = -70.162235930172$$
$$x_{31} = -64.9262481741891$$
$$x_{13} = -63.8790506229925$$
$$x_{33} = -58.6430628670095$$
$$x_{60} = -57.5958653158129$$
$$x_{70} = -52.3598775598299$$
$$x_{32} = -51.3126800086333$$
$$x_{12} = -46.0766922526503$$
$$x_{10} = -45.0294947014537$$
$$x_{71} = -39.7935069454707$$
$$x_{26} = -38.7463093942741$$
$$x_{38} = -33.5103216382911$$
$$x_{15} = -32.4631240870945$$
$$x_{36} = -27.2271363311115$$
$$x_{52} = -26.1799387799149$$
$$x_{45} = -20.943951023932$$
$$x_{1} = -19.8967534727354$$
$$x_{8} = -14.6607657167524$$
$$x_{44} = -13.6135681655558$$
$$x_{14} = -8.37758040957278$$
$$x_{29} = -7.33038285837618$$
$$x_{6} = -2.0943951023932$$
$$x_{64} = -1.0471975511966$$
$$x_{42} = 4.18879020478639$$
$$x_{17} = 5.23598775598299$$
$$x_{25} = 10.471975511966$$
$$x_{41} = 11.5191730631626$$
$$x_{24} = 16.7551608191456$$
$$x_{63} = 17.8023583703422$$
$$x_{22} = 23.0383461263252$$
$$x_{2} = 24.0855436775217$$
$$x_{34} = 29.3215314335047$$
$$x_{39} = 30.3687289847013$$
$$x_{62} = 35.6047167406843$$
$$x_{46} = 36.6519142918809$$
$$x_{59} = 41.8879020478639$$
$$x_{27} = 42.9350995990605$$
$$x_{58} = 48.1710873550435$$
$$x_{7} = 49.2182849062401$$
$$x_{11} = 54.4542726622231$$
$$x_{35} = 55.5014702134197$$
$$x_{19} = 60.7374579694027$$
$$x_{50} = 61.7846555205993$$
$$x_{68} = 67.0206432765823$$
$$x_{30} = 68.0678408277789$$
$$x_{51} = 73.3038285837618$$
$$x_{23} = 74.3510261349584$$
$$x_{49} = 79.5870138909414$$
$$x_{69} = 80.634211442138$$
$$x_{53} = 85.870199198121$$
$$x_{9} = 86.9173967493176$$
$$x_{67} = 92.1533845053006$$
$$x_{37} = 93.2005820564972$$
$$x_{55} = 98.4365698124802$$
$$x_{65} = 99.4837673636768$$
$$x_{61} = 393.746279249921$$
is the points with change the sign of the inequality expression.
First define with the sign to the leftmost point:
$$x_{0} < x_{47}$$
For example, let's take the point
$$x_{0} = x_{47} - \frac{1}{10}$$
=
$$-11851.1346868919 - \frac{1}{10}$$
=
$$-11851.2346868919$$
substitute to the expression
$$\sin{\left(t \right)} < \frac{\left(-1\right) \sqrt{3}}{2}$$
$$\sin{\left(t \right)} < \frac{\left(-1\right) \sqrt{3}}{2}$$

            ___ 
         -\/ 3  
sin(t) < -------
            2   
         

Then
$$x < -11851.1346868919$$
no execute
one of the solutions of our inequality is:
$$x > -11851.1346868919 \wedge x < -5606.69568910658$$

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       x_47      x_56      x_48      x_40      x_16      x_3      x_66      x_4      x_43      x_5      x_18      x_54      x_57      x_21      x_20      x_28      x_31      x_13      x_33      x_60      x_70      x_32      x_12      x_10      x_71      x_26      x_38      x_15      x_36      x_52      x_45      x_1      x_8      x_44      x_14      x_29      x_6      x_64      x_42      x_17      x_25      x_41      x_24      x_63      x_22      x_2      x_34      x_39      x_62      x_46      x_59      x_27      x_58      x_7      x_11      x_35      x_19      x_50      x_68      x_30      x_51      x_23      x_49      x_69      x_53      x_9      x_67      x_37      x_55      x_65      x_61

Other solutions will get with the changeover to the next point
etc.
The answer:
$$x > -11851.1346868919 \wedge x < -5606.69568910658$$
$$x > -1559.27715373173 \wedge x < -151.843644923507$$
$$x > -114.144533080429 \wedge x < -101.57816246607$$
$$x > -96.342174710087 \wedge x < -95.2949771588904$$
$$x > -90.0589894029074 \wedge x < -89.0117918517108$$
$$x > -83.7758040957278 \wedge x < -82.7286065445312$$
$$x > -77.4926187885482 \wedge x < -76.4454212373516$$
$$x > -71.2094334813686 \wedge x < -70.162235930172$$
$$x > -64.9262481741891 \wedge x < -63.8790506229925$$
$$x > -58.6430628670095 \wedge x < -57.5958653158129$$
$$x > -52.3598775598299 \wedge x < -51.3126800086333$$
$$x > -46.0766922526503 \wedge x < -45.0294947014537$$
$$x > -39.7935069454707 \wedge x < -38.7463093942741$$
$$x > -33.5103216382911 \wedge x < -32.4631240870945$$
$$x > -27.2271363311115 \wedge x < -26.1799387799149$$
$$x > -20.943951023932 \wedge x < -19.8967534727354$$
$$x > -14.6607657167524 \wedge x < -13.6135681655558$$
$$x > -8.37758040957278 \wedge x < -7.33038285837618$$
$$x > -2.0943951023932 \wedge x < -1.0471975511966$$
$$x > 4.18879020478639 \wedge x < 5.23598775598299$$
$$x > 10.471975511966 \wedge x < 11.5191730631626$$
$$x > 16.7551608191456 \wedge x < 17.8023583703422$$
$$x > 23.0383461263252 \wedge x < 24.0855436775217$$
$$x > 29.3215314335047 \wedge x < 30.3687289847013$$
$$x > 35.6047167406843 \wedge x < 36.6519142918809$$
$$x > 41.8879020478639 \wedge x < 42.9350995990605$$
$$x > 48.1710873550435 \wedge x < 49.2182849062401$$
$$x > 54.4542726622231 \wedge x < 55.5014702134197$$
$$x > 60.7374579694027 \wedge x < 61.7846555205993$$
$$x > 67.0206432765823 \wedge x < 68.0678408277789$$
$$x > 73.3038285837618 \wedge x < 74.3510261349584$$
$$x > 79.5870138909414 \wedge x < 80.634211442138$$
$$x > 85.870199198121 \wedge x < 86.9173967493176$$
$$x > 92.1533845053006 \wedge x < 93.2005820564972$$
$$x > 98.4365698124802 \wedge x < 99.4837673636768$$
$$x > 393.746279249921$$