Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin^{2}{\left(2 x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \frac{\pi}{2}$$
Numerical solution$$x_{1} = -29.8451301000724$$
$$x_{2} = 89.5353906153414$$
$$x_{3} = 78.5398162225044$$
$$x_{4} = 37.6991119665793$$
$$x_{5} = 48.6946860958663$$
$$x_{6} = -14.1371668484631$$
$$x_{7} = -58.1194645366003$$
$$x_{8} = -17.2787595621355$$
$$x_{9} = -94.247779486083$$
$$x_{10} = -21.9911485864927$$
$$x_{11} = 29.8451303084991$$
$$x_{12} = 59.690260541069$$
$$x_{13} = -1.57079642013166$$
$$x_{14} = -97.3893723711949$$
$$x_{15} = 21.9911485851564$$
$$x_{16} = -80.1106125854791$$
$$x_{17} = 28.2743338652921$$
$$x_{18} = 51.8362788866811$$
$$x_{19} = -7.85398150696156$$
$$x_{20} = 4.71238898608896$$
$$x_{21} = 72.2566310277248$$
$$x_{22} = 7.85398173011892$$
$$x_{23} = -73.8274272808521$$
$$x_{24} = -72.2566309100272$$
$$x_{25} = -51.8362786915081$$
$$x_{26} = 26.7035375390573$$
$$x_{27} = 56.5486676469942$$
$$x_{28} = -42.4115007432387$$
$$x_{29} = 70.6858346557926$$
$$x_{30} = -75.3982237985682$$
$$x_{31} = 6.28318528443138$$
$$x_{32} = 86.3937978937855$$
$$x_{33} = 15.7079633917898$$
$$x_{34} = 34.5575190717885$$
$$x_{35} = -81.6814090370675$$
$$x_{36} = 94.247779609353$$
$$x_{37} = 14.1371670778185$$
$$x_{38} = 117.809724442492$$
$$x_{39} = -1.57079626356835$$
$$x_{40} = 36.1283154718409$$
$$x_{41} = 1.57079638652515$$
$$x_{42} = -31.4159266517141$$
$$x_{43} = 100.530964798296$$
$$x_{44} = -28.2743337586152$$
$$x_{45} = -15.7079632962205$$
$$x_{46} = 72.256630710694$$
$$x_{47} = -36.128315427252$$
$$x_{48} = -95.818575868455$$
$$x_{49} = -97.3893725907902$$
$$x_{50} = -6.28318518328035$$
$$x_{51} = -37.6991118766796$$
$$x_{52} = -83.2522051669813$$
$$x_{53} = -50.2654823342013$$
$$x_{54} = 42.4115007365289$$
$$x_{55} = -53.4070752253874$$
$$x_{56} = -43.9822971747455$$
$$x_{57} = -20.4203521774723$$
$$x_{58} = 81.6814091152362$$
$$x_{59} = 45.5530935075531$$
$$x_{60} = -23.5619449982306$$
$$x_{61} = 12.5663704969137$$
$$x_{62} = 67.5442420634706$$
$$x_{63} = 50.2654824463816$$
$$x_{64} = -58.1194640062544$$
$$x_{65} = -86.3937978789102$$
$$x_{66} = -39.2699081045218$$
$$x_{67} = 20.4203521581227$$
$$x_{68} = -67.5442421539445$$
$$x_{69} = -59.6902604569585$$
$$x_{70} = 0$$
$$x_{71} = -65.9734457653935$$
$$x_{72} = -61.2610566398387$$
$$x_{73} = 73.8274274646672$$
$$x_{74} = -100.530965206253$$
$$x_{75} = 95.8185760424586$$
$$x_{76} = -89.5353907315491$$
$$x_{77} = 64.4026493150839$$
$$x_{78} = 80.1106131511482$$
$$x_{79} = 65.9734457525462$$
$$x_{80} = 92.6769832182628$$
$$x_{81} = 87.9645943351391$$
$$x_{82} = -64.402649310466$$
$$x_{83} = -45.5530935761698$$
$$x_{84} = -9.42477807759933$$
$$x_{85} = 43.9822971692691$$
$$x_{86} = 95.8185756842062$$
$$x_{87} = 23.5619449483644$$
$$x_{88} = -87.9645943594276$$