$\sqrt 3 \cos 2x +\sin 2x -4\cos x +\sqrt 3 -(\sqrt 3 \cos x +\sin x -2)=0$
$\Leftrightarrow 2\sqrt 3 \cos^2 x - \sqrt 3 +2\sin x \cos x -4\cos x +\sqrt 3 -(\sqrt 3 \cos x +\sin x -2)=0$
$\Leftrightarrow 2\cos x (\sqrt 3 \cos x +\sin x -2) -(\sqrt 3 \cos x +\sin x -2)=0$
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