Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$2 \sin{\left(x \right)} - \cos^{2}{\left(x \right)} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 2 \operatorname{atan}{\left(1 + \sqrt{2} + \sqrt{2} \sqrt{1 + \sqrt{2}} \right)}$$
$$x_{2} = 2 \operatorname{atan}{\left(- \sqrt{2} \sqrt{1 + \sqrt{2}} + 1 + \sqrt{2} \right)}$$
Numerical solution$$x_{1} = 94.6748581940863$$
$$x_{2} = -18.4224773351463$$
$$x_{3} = 25.5598198151108$$
$$x_{4} = -91.5332655404965$$
$$x_{5} = 69.5421169653679$$
$$x_{6} = 71.8295524461728$$
$$x_{7} = -631.887201957941$$
$$x_{8} = -85.2500802333169$$
$$x_{9} = 65.5463671389932$$
$$x_{10} = 38.12619042947$$
$$x_{11} = 82.1084875797271$$
$$x_{12} = -72.6837096189577$$
$$x_{13} = -30.9888479495055$$
$$x_{14} = -97.8164508476761$$
$$x_{15} = -16.1350418543414$$
$$x_{16} = 2.71451406719732$$
$$x_{17} = -37.272033256685$$
$$x_{18} = 8.9976993743769$$
$$x_{19} = 50.6925610438292$$
$$x_{20} = -41.2677830830598$$
$$x_{21} = 78.1127377533523$$
$$x_{22} = 84.3959230605319$$
$$x_{23} = -62.4047744854034$$
$$x_{24} = -43.5552185638646$$
$$x_{25} = -5.85610672078711$$
$$x_{26} = 31.8430051222904$$
$$x_{27} = -110.382821462035$$
$$x_{28} = -22.418227161521$$
$$x_{29} = -81.2543304069421$$
$$x_{30} = 52.979996524634$$
$$x_{31} = -100.103886328481$$
$$x_{32} = 100.958043501266$$
$$x_{33} = -49.8384038710442$$
$$x_{34} = 75.8253022725475$$
$$x_{35} = -9.85185654716186$$
$$x_{36} = 96.9622936748911$$
$$x_{37} = -28.7014124687006$$
$$x_{38} = -68.687959792583$$
$$x_{39} = 6.71026389357206$$
$$x_{40} = -122.949192076394$$
$$x_{41} = -47.5509683902394$$
$$x_{42} = -34.9845977758802$$
$$x_{43} = -12.1392920279667$$
$$x_{44} = 44.4093757366496$$
$$x_{45} = -3.56867123998227$$
$$x_{46} = -78.9668949261373$$
$$x_{47} = 46.6968112174544$$
$$x_{48} = 27.8472552959157$$
$$x_{49} = -66.4005243117781$$
$$x_{50} = 56.9757463510088$$
$$x_{51} = -56.1215891782238$$
$$x_{52} = 0.427078586392476$$
$$x_{53} = -87.5375157141217$$
$$x_{54} = -93.8207010213013$$
$$x_{55} = 34.1304406030953$$
$$x_{56} = 12.9934492007516$$
$$x_{57} = 15.2808846815565$$
$$x_{58} = -53.834153697419$$
$$x_{59} = 40.4136259102748$$
$$x_{60} = 19.2766345079312$$
$$x_{61} = -60.1173390045985$$
$$x_{62} = 88.3916728869067$$
$$x_{63} = -74.9711450997626$$
$$x_{64} = 59.2631818318136$$
$$x_{65} = -24.7056626423259$$
$$x_{66} = 90.6791083677115$$
$$x_{67} = 63.2589316581883$$
$$x_{68} = 21.5640699887361$$