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PT
$\Leftrightarrow \sqrt{3}(2\cos^{2}x-2)+\sqrt 3 \cos x +3\sin x-2\sin x\cos x=0$
$\Leftrightarrow -2\sqrt{3}\sin^2 x+\sqrt 3 \cos x +3\sin x-2\sin x\cos x=0$
$\Leftrightarrow -\sqrt{3}\sin x(2\sin x-\sqrt 3)-\cos x(2\sin x-\sqrt 3)=0$
$\Leftrightarrow (\sqrt 3\sin x+\cos x)(2\sin x-\sqrt 3)=0$
$\Leftrightarrow \left[ {\begin{matrix} \sqrt 3\sin x+\cos x=0\\ 2\sin x-\sqrt 3=0 \end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix}\sin(x+\dfrac{\pi}{6})=0\\ \sin x=\dfrac{\sqrt 3}{2} \end{matrix}} \right.$
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