[tex]\displaystyle\\
\frac{\sin x +2\cos x}{3} =\sin x ~~~\Big| \cdot 3 \\\\
\sin x + 2\cos x = 3\sin x\\\\
2\cos x = 3\sin x - \sin x\\\\
2\cos x = 2\sin x ~~~\Big| : 2 \\\\
\cos x = \sin x~~~\Big| : \sin x\\\\
\frac{\cos x}{\sin x} = 1\\\\
\text{ctg}\,x = 1 \\\\
x = \text{arcctg}(1) = \boxed{\bf \frac{\pi}{4} } = \boxed{\bf 45^o} \in [0; \pi][/tex]
