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$$x_{1} = 12.5663706143592$$
$$x_{2} = 97.389506033414$$
$$x_{3} = -28.2742611423571$$
$$x_{4} = 37.6991118430775$$
$$x_{5} = 72.2566292957295$$
$$x_{6} = -91.1063173161218$$
$$x_{7} = 72.2564974285085$$
$$x_{8} = -72.2565620594227$$
$$x_{9} = -31.4159265358979$$
$$x_{10} = 0$$
$$x_{11} = 84.8228826659845$$
$$x_{12} = -50.2654824574367$$
$$x_{13} = -53.4071523808127$$
$$x_{14} = 6.28318530717959$$
$$x_{15} = -94.2477796076938$$
$$x_{16} = -69.1150383789755$$
$$x_{17} = -59.6902836920888$$
$$x_{18} = 53.4072061236969$$
$$x_{19} = -34.5573938477265$$
$$x_{20} = 65.9735385828884$$
$$x_{21} = 62.8318530717959$$
$$x_{22} = 50.2654824574367$$
$$x_{23} = 81.6814089933346$$
$$x_{24} = 100.530964914873$$
$$x_{25} = -87.9645943005142$$
$$x_{26} = -65.9734547074718$$
$$x_{27} = 72.2566368440238$$
$$x_{28} = -9.42485173622935$$
$$x_{29} = -59.6902757594272$$
$$x_{30} = 78.5397496778866$$
$$x_{31} = -15.7079741551755$$
$$x_{32} = -56.5486677646163$$
$$x_{33} = 28.2742362262029$$
$$x_{34} = -37.6991118430775$$
$$x_{35} = -25.1327412287183$$
$$x_{36} = -97.3894529845737$$
$$x_{37} = -100.530964914873$$
$$x_{38} = -1083.8495084391$$
$$x_{39} = -75.398223686155$$
$$x_{40} = 18.8495559215388$$
$$x_{41} = 28.2743275355147$$
$$x_{42} = 34.557448949744$$
$$x_{43} = 59.6903404916682$$
$$x_{44} = 65.9734548161256$$
$$x_{45} = -6.28318530717959$$
$$x_{46} = -3.14171741723949$$
$$x_{47} = 9.42490616313103$$
$$x_{48} = -15.7080226365019$$
$$x_{49} = 56.5486677646163$$
$$x_{50} = -43.9822971502571$$
$$x_{51} = -47.1240173901594$$
$$x_{52} = 21.9912781084223$$
$$x_{53} = 15.7080397066029$$
$$x_{54} = 31.4159265358979$$
$$x_{55} = 94.2477796076938$$
$$x_{56} = -12.5663706143592$$
$$x_{57} = -78.5396939083992$$
$$x_{58} = 75.398223686155$$
$$x_{59} = 40.8405826017537$$
$$x_{60} = -21.9911516405744$$
$$x_{61} = 21.9911516419074$$
$$x_{62} = -81.6814089933346$$
$$x_{63} = 43.9822971502571$$
$$x_{64} = 87.9645943005142$$