Graph of the function intersects the axis X at f = 0
so we need to solve the equation:
$$\sin{\left(x \right)} - \frac{\sin{\left(2 x \right)}}{2} = 0$$
Solve this equationThe points of intersection with the axis X:
Analytical solution$$x_{1} = 0$$
$$x_{2} = \pi$$
Numerical solution$$x_{1} = 72.2566310325652$$
$$x_{2} = -87.9646059734436$$
$$x_{3} = -3.14159265358979$$
$$x_{4} = -31.4160020636547$$
$$x_{5} = 6.28317667998233$$
$$x_{6} = 40.8407044966673$$
$$x_{7} = 94.2477801894829$$
$$x_{8} = -91.106186954104$$
$$x_{9} = -15.707963267949$$
$$x_{10} = 31.4160561497334$$
$$x_{11} = -6.28311070964686$$
$$x_{12} = 53.4070751110265$$
$$x_{13} = 84.8230016469244$$
$$x_{14} = -47.1238898038469$$
$$x_{15} = -53.4070751110265$$
$$x_{16} = -100.530843957291$$
$$x_{17} = -94.2477125450604$$
$$x_{18} = 12.5662986015402$$
$$x_{19} = -9.42477796076938$$
$$x_{20} = -37.6991527323202$$
$$x_{21} = 37.6991667998317$$
$$x_{22} = 37.699190106891$$
$$x_{23} = 15.707963267949$$
$$x_{24} = 75.3983560849494$$
$$x_{25} = -75.398302687768$$
$$x_{26} = 97.3893722612836$$
$$x_{27} = -25.1328674095127$$
$$x_{28} = 78.5398163397448$$
$$x_{29} = 87.9646063176306$$
$$x_{30} = 9.42477796076938$$
$$x_{31} = 62.8317326282647$$
$$x_{32} = 100.53090005808$$
$$x_{33} = -34.5575191894877$$
$$x_{34} = -28.2743338823081$$
$$x_{35} = 56.5485993084863$$
$$x_{36} = -78.5398163397448$$
$$x_{37} = 59.6902604182061$$
$$x_{38} = -12.566243836043$$
$$x_{39} = 43.9823032538019$$
$$x_{40} = -37.6991249685283$$
$$x_{41} = -21.9911485751286$$
$$x_{42} = -81.6814156709145$$
$$x_{43} = 18.8494325865513$$
$$x_{44} = -72.2566310325652$$
$$x_{45} = 75.3983371038378$$
$$x_{46} = 28.2743338823081$$
$$x_{47} = 6.28310686972697$$
$$x_{48} = 81.6814908613415$$
$$x_{49} = 50.2653660953425$$
$$x_{50} = -97.3893722612836$$
$$x_{51} = 43.982408931344$$
$$x_{52} = 65.9734457253857$$
$$x_{53} = 87.9646679208845$$
$$x_{54} = -65.9734457253857$$
$$x_{55} = -56.5485438718624$$
$$x_{56} = 0$$
$$x_{57} = -59.6902604182061$$
$$x_{58} = 34.5575191894877$$
$$x_{59} = -69.1151673590674$$
$$x_{60} = 50.2654784088459$$
$$x_{61} = -43.9823032324142$$
$$x_{62} = 21.9911485751286$$
$$x_{63} = -50.2654115920793$$
$$x_{64} = -81.6814265277516$$