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PT $\Leftrightarrow \cos3x+\sqrt{3}\sin 3x=\sqrt{3}\cos x+\sin x$
$\Leftrightarrow \frac{1}{2}\cos3x+\frac{\sqrt{3}}{2}\sin 3x=\frac{\sqrt{3}}{2}\cos x+\frac{1}{2}\sin x$
$\Leftrightarrow \sin\frac{\pi}{6}\cos3x+\cos\frac{\pi}{6}\sin 3x= \sin\frac{\pi}{3}\cos x+\cos\frac{\pi}{3}\sin x$
$\Leftrightarrow \sin \left ( 3x +\frac{\pi}{6}\right )=\sin \left ( x +\frac{\pi}{3}\right )$
$\Leftrightarrow \left[ {\begin{matrix} 3x +\frac{\pi}{6}=x +\frac{\pi}{3} +k2\pi\\ 3x +\frac{\pi}{6}=\pi-x -\frac{\pi}{3} +k2\pi\end{matrix}} \right.$
$\Leftrightarrow \left[ {\begin{matrix} x=\frac{\pi}{12} +k\pi\\ x = -\frac{\pi}{8} +k\frac{\pi}{2} \end{matrix}} \right. (k \in \mathbb{Z})$
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