For $\sin 2x+\cos x =0,$ use a double-angle or half-angle formula to simplify the equation and then find all solutions of the equation in the interval $[0,2\pi).$
The answer is $x_1=$ , $x_2=$ , $x_3=$ and $x_4=$ with $x_1<x_2<x_3<x_4$.