2sinx-корень3tgx-2корень3cosx+3=0

Решите задачу:

$2\sin x- \sqrt{3} tg x-2\sqrt{3}\cos x+3=0|\cdot (\cos x\ne 0)\\ \\ 2\sin x\cos x-\sqrt{3}\sin x-2\sqrt{3}\cos^2 x+3\cos x=0\\ \\ \sin x(2\cos x-\sqrt{3})-\sqrt{3}\cos x(2\cos x-\sqrt{3})=0\\ \\ (2\cos x-\sqrt{3})(\sin -\sqrt{3}\cos x)=0\\ \\ 2\cos x-\sqrt{3}=0\\ \\ \cos x= \frac{\sqrt{3}}{2} \\ \\ \boxed{x_1=\pm \frac{\pi}{6}+ 2\pi n,n \in Z}\\ \\ \\ \sin x-\sqrt{3}\cos x=0|:\cos x\\ \\ tg x=\sqrt{3}\\ \\ \boxed{x_2= \frac{\pi}{3}+ \pi n,n \in Z }$