Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\cos{\left(2 x + \frac{\pi}{6} \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \frac{\pi}{6}$$
$$x_{2} = \frac{2 \pi}{3}$$
Numerical solution$$x_{1} = 17.8023583703422$$
$$x_{2} = -35.6047167406843$$
$$x_{3} = 75.9218224617533$$
$$x_{4} = 22.5147473507269$$
$$x_{5} = 96.342174710087$$
$$x_{6} = -10.471975511966$$
$$x_{7} = -48.1710873550435$$
$$x_{8} = 2.0943951023932$$
$$x_{9} = -41.8879020478639$$
$$x_{10} = -85.870199198121$$
$$x_{11} = 66.497044500984$$
$$x_{12} = 0.523598775598299$$
$$x_{13} = -4.18879020478639$$
$$x_{14} = 77.4926187885482$$
$$x_{15} = -87.4409955249159$$
$$x_{16} = 38.2227106186758$$
$$x_{17} = -18.3259571459405$$
$$x_{18} = 52.3598775598299$$
$$x_{19} = 39.7935069454707$$
$$x_{20} = 69.6386371545737$$
$$x_{21} = -92.1533845053006$$
$$x_{22} = 99.4837673636768$$
$$x_{23} = -34.0339204138894$$
$$x_{24} = 33.5103216382911$$
$$x_{25} = -54.4542726622231$$
$$x_{26} = -40.317105721069$$
$$x_{27} = 91.6297857297023$$
$$x_{28} = 68.0678408277789$$
$$x_{29} = -62.3082542961976$$
$$x_{30} = -13.6135681655558$$
$$x_{31} = -57.5958653158129$$
$$x_{32} = -78.0162175641465$$
$$x_{33} = -19.8967534727354$$
$$x_{34} = -43.4586983746588$$
$$x_{35} = -71.733032256967$$
$$x_{36} = 8.37758040957278$$
$$x_{37} = 44.5058959258554$$
$$x_{38} = 53.9306738866248$$
$$x_{39} = 3.66519142918809$$
$$x_{40} = 88.4881930761125$$
$$x_{41} = -16.7551608191456$$
$$x_{42} = 94.7713783832921$$
$$x_{43} = 60.2138591938044$$
$$x_{44} = 47.6474885794452$$
$$x_{45} = -5.75958653158129$$
$$x_{46} = 80.634211442138$$
$$x_{47} = -84.2994028713261$$
$$x_{48} = 25.6563400043166$$
$$x_{49} = -26.1799387799149$$
$$x_{50} = 58.6430628670095$$
$$x_{51} = 46.0766922526503$$
$$x_{52} = -21.4675497995303$$
$$x_{53} = 82.2050077689329$$
$$x_{54} = -79.5870138909414$$
$$x_{55} = -32.4631240870945$$
$$x_{56} = -51.3126800086333$$
$$x_{57} = 55.5014702134197$$
$$x_{58} = 30.3687289847013$$
$$x_{59} = 61.7846555205993$$
$$x_{60} = -29.3215314335047$$
$$x_{61} = 83.7758040957278$$
$$x_{62} = -93.7241808320955$$
$$x_{63} = -70.162235930172$$
$$x_{64} = -95.2949771588904$$
$$x_{65} = -98.4365698124802$$
$$x_{66} = -49.7418836818384$$
$$x_{67} = 1228.88632632921$$
$$x_{68} = -100.007366139275$$
$$x_{69} = 31.9395253114962$$
$$x_{70} = 9.94837673636768$$
$$x_{71} = -56.025068989018$$
$$x_{72} = 24.0855436775217$$
$$x_{73} = 74.3510261349584$$
$$x_{74} = 97.9129710368819$$
$$x_{75} = 36.6519142918809$$
$$x_{76} = -12.0427718387609$$
$$x_{77} = -27.7507351067098$$
$$x_{78} = 90.0589894029074$$
$$x_{79} = -73.3038285837618$$
$$x_{80} = -7.33038285837618$$
$$x_{81} = 14.6607657167524$$
$$x_{82} = 11.5191730631626$$
$$x_{83} = -63.8790506229925$$
$$x_{84} = 16.2315620435473$$
$$x_{85} = 27.2271363311115$$
$$x_{86} = -76.4454212373516$$
$$x_{87} = -65.4498469497874$$