Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\log{\left(\sin^{2}{\left(x \right)} \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = - \frac{\pi}{2}$$
$$x_{2} = \frac{\pi}{2}$$
$$x_{3} = \frac{3 \pi}{2}$$
Numerical solution$$x_{1} = 83.2522046133019$$
$$x_{2} = 98.960168163288$$
$$x_{3} = 54.9778709996295$$
$$x_{4} = -14.1371668348969$$
$$x_{5} = -92.6769840888992$$
$$x_{6} = 42.4115007257882$$
$$x_{7} = -80.1106125767506$$
$$x_{8} = 48.6946858781977$$
$$x_{9} = 20.4203521458531$$
$$x_{10} = 89.5353909237568$$
$$x_{11} = 61.2610572372815$$
$$x_{12} = -4.71238851018714$$
$$x_{13} = 14.1371671149845$$
$$x_{14} = -1.57079643406453$$
$$x_{15} = 83.2522058199769$$
$$x_{16} = 67.5442423431831$$
$$x_{17} = 51.8362789063255$$
$$x_{18} = -58.1194639960442$$
$$x_{19} = -26.7035370924819$$
$$x_{20} = 1.57079660167231$$
$$x_{21} = -70.6858354999348$$
$$x_{22} = -20.420351978766$$
$$x_{23} = 70.6858344584179$$
$$x_{24} = 95.8185760669056$$
$$x_{25} = -29.8451300946193$$
$$x_{26} = -45.5530935938585$$
$$x_{27} = 7.85398174556756$$
$$x_{28} = -48.6946856746846$$
$$x_{29} = -32.9867221000851$$
$$x_{30} = 26.7035372979479$$
$$x_{31} = -54.9778719110131$$
$$x_{32} = -54.9778706878326$$
$$x_{33} = -70.6858342567981$$
$$x_{34} = 17.2787600722029$$
$$x_{35} = -73.827427279653$$
$$x_{36} = 32.9867224176774$$
$$x_{37} = -4.71238973521995$$
$$x_{38} = -76.969020493421$$
$$x_{39} = -39.2699084429902$$
$$x_{40} = 76.9690208439152$$
$$x_{41} = 45.5530937626454$$
$$x_{42} = 80.110613129539$$
$$x_{43} = 39.2699074396221$$
$$x_{44} = 86.393797885724$$
$$x_{45} = 73.8274274866345$$
$$x_{46} = -36.1283154154305$$
$$x_{47} = -61.2610570233699$$
$$x_{48} = 10.9955738356399$$
$$x_{49} = 61.2610560266003$$
$$x_{50} = 98.9601694339084$$
$$x_{51} = -92.6769828388254$$
$$x_{52} = -86.3937977199047$$
$$x_{53} = -98.9601678624104$$
$$x_{54} = 54.9778722543492$$
$$x_{55} = -10.9955747464857$$
$$x_{56} = -10.9955735120111$$
$$x_{57} = -67.5442421737401$$
$$x_{58} = -17.2787598626449$$
$$x_{59} = -48.6946869113465$$
$$x_{60} = -98.9601690759292$$
$$x_{61} = 17.2787588523536$$
$$x_{62} = 76.9690195814988$$
$$x_{63} = -26.7035383231143$$
$$x_{64} = 10.9955750764068$$
$$x_{65} = -64.402649139553$$
$$x_{66} = -42.4115005591739$$
$$x_{67} = 29.8451303259723$$
$$x_{68} = 4.71238871766746$$
$$x_{69} = 39.2699086546913$$
$$x_{70} = -76.9690192752694$$
$$x_{71} = 36.1283156368797$$
$$x_{72} = -32.9867233287024$$
$$x_{73} = -51.8362786889121$$
$$x_{74} = -95.818575867973$$
$$x_{75} = -23.5619450139675$$
$$x_{76} = 32.9867236651869$$
$$x_{77} = 23.5619451821423$$
$$x_{78} = 58.119464370396$$
$$x_{79} = 92.6769830386097$$
$$x_{80} = -83.252205603785$$
$$x_{81} = -89.5353907536146$$
$$x_{82} = 64.402649305744$$
$$x_{83} = -7.85398149475684$$