$\begin{array}{l}
2{\sin ^2}x + \sqrt 3 \sin 2x - 2\left( {\sqrt 3 \sin x + \cos x} \right) - 7 = 0\,\,\left( * \right)\\
Dat\,\sqrt 3 \sin x + \cos x = t\left( { - 2 \le t \le 2} \right)\,thi:\\
{t^2} = 3{\sin ^2}x + 2\sqrt 3 \sin x\cos x + {\cos ^2}x = 2{\sin ^2}x + \sqrt 3 \sin 2x + 1\\
\Rightarrow 2{\sin ^2}x + \sqrt 3 \sin 2x = {t^2} - 1\\
\Rightarrow \left( * \right) \Leftrightarrow {t^2} - 1 - 2t - 7 = 0 \Leftrightarrow {t^2} - 2t - 8 = 0 \Leftrightarrow \left[ \begin{array}{l}
t = - 2\left( {TM} \right)\\
t = 4\left( {loai} \right)
\end{array} \right.\\
\Rightarrow \sqrt 3 \sin x + \cos x = - 2 \Leftrightarrow \frac{{\sqrt 3 }}{2}\sin x + \frac{1}{2}\cos x = - 1\\
\Leftrightarrow \sin \left( {x + \frac{\pi }{6}} \right) = \sin \left( { - \frac{\pi }{2}} \right) \Leftrightarrow x + \frac{\pi }{6} = - \frac{\pi }{2} + k2\pi \Leftrightarrow x = - \frac{{2\pi }}{3} + k2\pi
\end{array}$
