Pt $\Leftrightarrow (\sqrt{3}sinx + cosx)(\sqrt{3}sinx - cosx) + \sqrt{3}sinx + cosx =0$$\Leftrightarrow ( \sqrt{3}sinx + cosx)( \sqrt{3}sinx - cosx +1)=0$
$\Leftrightarrow sin(x + \frac{\pi }{6}) =0 , sin(x-\frac{\pi }{6})= \frac{-1}{2}=sin\frac{\pi }{6}$
$\Leftrightarrow x= \frac{-\pi }{6} + k\pi , x=\frac{\pi }{3}+ k2\pi , x=\pi + k2\pi , k \in Z$