Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$4 \sin^{2}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \pi$$
Numerical solution$$x_{1} = 12.5663704518704$$
$$x_{2} = -25.132741473063$$
$$x_{3} = -37.6991118771514$$
$$x_{4} = 87.9645943357576$$
$$x_{5} = -31.4159267051849$$
$$x_{6} = 43.982297169427$$
$$x_{7} = -78.5398160958028$$
$$x_{8} = 6.28318528425126$$
$$x_{9} = -31.4159267959754$$
$$x_{10} = -87.9645943587732$$
$$x_{11} = 81.6814091761104$$
$$x_{12} = -9.42477812668337$$
$$x_{13} = 34.5575190304759$$
$$x_{14} = 100.530964766599$$
$$x_{15} = -47.1238900492539$$
$$x_{16} = 50.2654824463473$$
$$x_{17} = 15.7079634406648$$
$$x_{18} = -75.3982238620294$$
$$x_{19} = -15.7079632965264$$
$$x_{20} = 0$$
$$x_{21} = -65.9734457650176$$
$$x_{22} = 3.14159287686128$$
$$x_{23} = 53.4070753627408$$
$$x_{24} = -69.1150386253436$$
$$x_{25} = -106.814150357553$$
$$x_{26} = 21.9911485851964$$
$$x_{27} = -21.9911485864515$$
$$x_{28} = -3.14159289677385$$
$$x_{29} = 91.1061871583643$$
$$x_{30} = -72.2566308741333$$
$$x_{31} = 37.6991120192083$$
$$x_{32} = 97.3893727097471$$
$$x_{33} = -34.5575189426108$$
$$x_{34} = -53.4070752836338$$
$$x_{35} = 25.1327414478072$$
$$x_{36} = 75.3982241944528$$
$$x_{37} = -62.8318528379059$$
$$x_{38} = 9.42477821024198$$
$$x_{39} = 84.8230014093114$$
$$x_{40} = 25.1327410188866$$
$$x_{41} = -43.9822971745789$$
$$x_{42} = 3.14159244884412$$
$$x_{43} = 47.123889589354$$
$$x_{44} = 94.2477796093525$$
$$x_{45} = -62.8318532583801$$
$$x_{46} = -28.2743337166085$$
$$x_{47} = -94.2477794529919$$
$$x_{48} = -18.8495561207399$$
$$x_{49} = 69.1150381602162$$
$$x_{50} = -1734.15914475848$$
$$x_{51} = -6.28318513794069$$
$$x_{52} = -18.8495556944209$$
$$x_{53} = 75.3982239388525$$
$$x_{54} = -81.6814090380061$$
$$x_{55} = 18.8495554002244$$
$$x_{56} = 69.1150385885879$$
$$x_{57} = -56.5486675191652$$
$$x_{58} = -3.14159311568248$$
$$x_{59} = 56.5486676091327$$
$$x_{60} = -97.3893724403711$$
$$x_{61} = 59.6902605976901$$
$$x_{62} = 78.5398161878405$$
$$x_{63} = -84.82300141007$$
$$x_{64} = -91.1061872003049$$
$$x_{65} = 31.4159267865366$$
$$x_{66} = 62.8318528326557$$
$$x_{67} = -91.106187201329$$
$$x_{68} = -34.5575189701076$$
$$x_{69} = 28.2743338652012$$
$$x_{70} = 65.9734457528975$$
$$x_{71} = -40.8407046898283$$
$$x_{72} = 18.8495556796107$$
$$x_{73} = 91.1061867314459$$
$$x_{74} = -69.1150386737158$$
$$x_{75} = -40.8407042660168$$
$$x_{76} = 97.3893725148693$$
$$x_{77} = 40.8407042560881$$
$$x_{78} = -100.530964672522$$
$$x_{79} = 53.4070756765307$$
$$x_{80} = -50.2654822953391$$
$$x_{81} = -12.5663703661411$$
$$x_{82} = 47.123890018392$$
$$x_{83} = 72.256631027719$$
$$x_{84} = -84.8230018263493$$
$$x_{85} = -59.6902604576401$$
$$x_{86} = -25.132741632083$$
$$x_{87} = -47.123890151099$$