Нужна помощь фото внизу

Решите задачу:

$\frac{\sin x}{\sin x-\cos x}=\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+tg2x\right)\\\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+tg2x\right)=\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+\frac{2}{ctgx-tgx}\right)=\\=\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+\frac{2}{\frac{\cos x}{\sin x}-\frac{\sin x}{\cos x}}\right)=\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+\frac{2}{\frac{\cos^2x-\sin^2x}{\sin x\cos x}}\right)=$
$=\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+\frac{2\sin x\cos x}{{\cos^2x-\sin^2x}{}}\right)=\\=\sqrt3\left(\frac{\cos x}{\sin x+\cos x}+\frac{2\sin x\cos x}{{(\cos x-\sin x)(\cos x+\sin x)}{}}\right)=\\=\sqrt3\left(\frac{\cos x(\cos x-\sin x)+2\sin x\cos x}{(\cos x-\sin x)(\cos x+\sin x)}\right)=\sqrt3\left(\frac{\cos^2x-\cos x\sin x+2\sin x\cos x}{(\cos x-\sin x)(\cos x+\sin x)}\right)=\\=\sqrt3\left(\frac{\cos x(\cos x+\sin x)}{(\cos x-\sin x)(\cos x+\sin x)}\right)=\sqrt3\cdot\frac{\cos x}{\cos x-\sin x}$
$\frac{\sin x}{\sin x-\cos x}=\sqrt3\frac{\cos x}{\cos x-\sin x}\\\frac{\sin x}{\sin x-\cos x}=-\sqrt3\frac{\cos x}{\sin x-\cos x}\\\frac{\sin x}{\cos x}=-\sqrt3\\tgx=-\sqrt3\Rightarrow x=\frac{2\pi}3+\pi n,\;n\in\mathbb{Z}$