Решите пожалуйста

Решите задачу:

$\sqrt{3}sin\frac{x}{4}-cos\frac{x}{4}=0\\ 2(\frac{\sqrt3}{2}sin\frac{x}{4}-\frac{1}{2}cos\frac{x}{4})=0\\\frac{\sqrt3}{2}=cos\frac{\pi}{6};\quad \frac{1}{2}=\sin\frac{\pi}{6}\\2(sin\frac{x}{4}cos\frac{\pi}{6}-cos\frac{x}{4}sin\frac{\pi}{6})=0\\sin(\frac{x}{4}-\frac{\pi}{6})=0\\ \frac{x}{4}-\frac{\pi}{6}=\pi n, \; n \in Z\\\frac{x}{4}=\frac{\pi}{6}+\pi n, \; n\in Z\\x=\frac{2\pi}{3}+4\pi n, \; n\in Z$