Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\left(3 \sin{\left(x \right)} - 1\right)^{2} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = \pi - \operatorname{asin}{\left(\frac{1}{3} \right)}$$
$$x_{2} = \operatorname{asin}{\left(\frac{1}{3} \right)}$$
Numerical solution$$x_{1} = -62.4920163818316$$
$$x_{2} = 21.6513118947153$$
$$x_{3} = -91.4460239984049$$
$$x_{4} = 34.2176823070459$$
$$x_{5} = -85.1628387089093$$
$$x_{6} = 46.7840531708765$$
$$x_{7} = 75.7380607328926$$
$$x_{8} = -47.4637268433349$$
$$x_{9} = -43.6424603108001$$
$$x_{10} = 94.5876163201449$$
$$x_{11} = 25.4725783035469$$
$$x_{12} = 97.0495354899038$$
$$x_{13} = 40.5008674830826$$
$$x_{14} = 56.8885043428558$$
$$x_{15} = 12.9062071864044$$
$$x_{16} = 46.7840527334435$$
$$x_{17} = -87.6247574715351$$
$$x_{18} = -18.5097188451844$$
$$x_{19} = -53.7469120227526$$
$$x_{20} = 38.0389486817881$$
$$x_{21} = 19.1893924382792$$
$$x_{22} = 63.1716895888171$$
$$x_{23} = 71.9167941971572$$
$$x_{24} = 75.7380609680837$$
$$x_{25} = -72.596467604548$$
$$x_{26} = -68.7752018610102$$
$$x_{27} = -28.614170448074$$
$$x_{28} = -9.76461485882572$$
$$x_{29} = 88.3044311727195$$
$$x_{30} = 19.1893926389477$$
$$x_{31} = 50.6053191608345$$
$$x_{32} = -62.4920159945506$$
$$x_{33} = -22.3309852645719$$
$$x_{34} = 69.454875000383$$
$$x_{35} = 44.322134011278$$
$$x_{36} = 6.62302200163617$$
$$x_{37} = -18.5097192576148$$
$$x_{38} = -41.1805415624178$$
$$x_{39} = 15.3681267081539$$
$$x_{40} = 31.75576357759$$
$$x_{41} = 25.4725778699293$$
$$x_{42} = -66.3132824240093$$
$$x_{43} = 27.9344970337768$$
$$x_{44} = -12.2265335780846$$
$$x_{45} = -5.94334854201109$$
$$x_{46} = -49.9256458942351$$
$$x_{47} = -81.3415723164028$$
$$x_{48} = -24.7929044293411$$
$$x_{49} = -91.4460242422282$$
$$x_{50} = 63.1716896783568$$
$$x_{51} = 2.80175603965811$$
$$x_{52} = -85.1628382296233$$
$$x_{53} = 84.4831646238282$$
$$x_{54} = -75.0583871257405$$
$$x_{55} = 78.1999794758049$$
$$x_{56} = 69.4548754515735$$
$$x_{57} = 82.0212458719137$$
$$x_{58} = -60.0300972962665$$
$$x_{59} = 59.3504238641263$$
$$x_{60} = -41.1805410939385$$
$$x_{61} = 100.870801499545$$
$$x_{62} = 0.339836850123862$$
$$x_{63} = -24.7929047116773$$
$$x_{64} = 2.80175558507591$$
$$x_{65} = -97.7292091852875$$
$$x_{66} = -68.7752015182258$$
$$x_{67} = -16.0478001305676$$
$$x_{68} = -3.48142968793679$$
$$x_{69} = -75.0583866330114$$
$$x_{70} = -37.3592751574448$$
$$x_{71} = -31.0760899697983$$
$$x_{72} = -56.2088307341417$$
$$x_{73} = -100.191127890597$$
$$x_{74} = 53.0672384317186$$
$$x_{75} = 40.500867467785$$
$$x_{76} = 90.7663498825822$$
$$x_{77} = 9.08494140709534$$
$$x_{78} = 65.6336090538507$$
$$x_{79} = 90.7663502993762$$