Graph of the function intersects the axis T at f = 0
so we need to solve the equation:
$$\frac{\sin^{2}{\left(t \right)}}{\sin{\left(t \right)} + 2} = 0$$
Solve this equationThe points of intersection with the axis T:
Analytical solution$$t_{1} = 0$$
$$t_{2} = \pi$$
Numerical solution$$t_{1} = -56.5486675835621$$
$$t_{2} = 3.14159312185834$$
$$t_{3} = -40.8407040289876$$
$$t_{4} = 53.4070757175476$$
$$t_{5} = 25.1327407744412$$
$$t_{6} = -50.2654823212533$$
$$t_{7} = -62.8318529476859$$
$$t_{8} = -37.6991126284565$$
$$t_{9} = 12.5663704137215$$
$$t_{10} = -97.3893724084397$$
$$t_{11} = -59.6902604559996$$
$$t_{12} = -12.566370432922$$
$$t_{13} = 78.5398162107716$$
$$t_{14} = 31.4159267173782$$
$$t_{15} = -84.8230011807336$$
$$t_{16} = 43.982297991191$$
$$t_{17} = -18.8495563752342$$
$$t_{18} = -75.3982239084087$$
$$t_{19} = -62.8318535236677$$
$$t_{20} = 31.4159264181377$$
$$t_{21} = -21.9911485863129$$
$$t_{22} = -81.6814090403179$$
$$t_{23} = 75.3982240661504$$
$$t_{24} = -31.4159267473569$$
$$t_{25} = 69.1150379252292$$
$$t_{26} = 15.7079634846579$$
$$t_{27} = -69.1150388783611$$
$$t_{28} = -91.1061871295728$$
$$t_{29} = -3.14159245222419$$
$$t_{30} = 87.9645943344402$$
$$t_{31} = 100.530964735934$$
$$t_{32} = -69.1150387611399$$
$$t_{33} = 25.1327413267662$$
$$t_{34} = 47.1238897117841$$
$$t_{35} = 75.3982238673193$$
$$t_{36} = 6.28318528365976$$
$$t_{37} = -47.1238895535581$$
$$t_{38} = 18.849555556969$$
$$t_{39} = 53.4070755016345$$
$$t_{40} = -65.9734457633727$$
$$t_{41} = 21.9911485853088$$
$$t_{42} = 72.2566310277446$$
$$t_{43} = -43.9822971752436$$
$$t_{44} = 75.3982235055873$$
$$t_{45} = -15.7079632956568$$
$$t_{46} = -72.2566308384363$$
$$t_{47} = -84.8230016739514$$
$$t_{48} = -40.8407045494855$$
$$t_{49} = 94.2477796093495$$
$$t_{50} = -34.5575188166549$$
$$t_{51} = 40.8407043200489$$
$$t_{52} = -94.2477794766245$$
$$t_{53} = -91.1061866630345$$
$$t_{54} = 50.265482446211$$
$$t_{55} = 59.6902606460951$$
$$t_{56} = -53.4070752540144$$
$$t_{57} = -3.14159283024245$$
$$t_{58} = -87.9645943627279$$
$$t_{59} = -81.6814088716349$$
$$t_{60} = -12.5663706569192$$
$$t_{61} = 43.9822971690315$$
$$t_{62} = 91.1061874205003$$
$$t_{63} = 97.3893726603459$$
$$t_{64} = -6.28318516617079$$
$$t_{65} = -78.5398159761873$$
$$t_{66} = 84.8230017192229$$
$$t_{67} = 28.274333865516$$
$$t_{68} = 81.6814091431634$$
$$t_{69} = 0$$
$$t_{70} = 65.9734457537561$$
$$t_{71} = -25.1327416022221$$
$$t_{72} = -56.5486677178641$$
$$t_{73} = -37.699111878477$$
$$t_{74} = 56.54866757482$$
$$t_{75} = -9.42477809933772$$
$$t_{76} = 34.5575190555905$$
$$t_{77} = -100.530964734526$$
$$t_{78} = 3.14159257938259$$
$$t_{79} = 9.42477834262643$$
$$t_{80} = -65.9734468967977$$
$$t_{81} = 62.8318527164084$$
$$t_{82} = -31.4159273869072$$
$$t_{83} = 37.6991119886324$$
$$t_{84} = -47.1238899801267$$
$$t_{85} = 84.8230014707211$$
$$t_{86} = 18.8495572418557$$
$$t_{87} = 91.1061868470564$$
$$t_{88} = -43.982298747563$$
$$t_{89} = -28.2743336768524$$
$$t_{90} = -18.8495558093765$$
$$t_{91} = 47.1238902717198$$
$$t_{92} = 40.840704639321$$
$$t_{93} = 103.672556339194$$
$$t_{94} = 69.1150384602719$$