$\sin 3x + \sqrt{3}\cos 3x + \cos 2x - \sqrt{3}\sin 2x = \sin x + \sqrt{3}\cos x$
$(\sin 3x -\sin x) + \sqrt 3(\cos 3x - \cos x) + ( \cos 2x - \sqrt{3}\sin 2x) =0$
$2\cos 2x \sin x - 2\sqrt 3 \sin 2x \sin x + ( \cos 2x - \sqrt{3}\sin 2x) =0$
$2\sin x ( \cos 2x - \sqrt{3}\sin 2x) + ( \cos 2x - \sqrt{3}\sin 2x) =0$
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