$\begin{array}{l}
2\sin x\cos x + \sqrt 3 - 2\cos x - \sqrt 3 \sin x = 0\\
\Leftrightarrow 2\cos x\left( {\sin x - 1} \right) - \sqrt 3 \left( {\sin x - 1} \right) = 0\\
\Leftrightarrow \left( {\sin x - 1} \right)\left( {2\cos x - \sqrt 3 } \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
\sin x = 1\\
\cos x = \dfrac{{\sqrt 3 }}{2}
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = \dfrac{\pi }{2} + k2\pi \\
x = \dfrac{\pi }{6} + k2\pi \\
x = - \dfrac{\pi }{2} + k2\pi
\end{array} \right.\left( {k \in \mathbb Z} \right)
\end{array}$