+$\sin 3x=3\sin x-4\sin^3x$+$\cos 3x=-(3\cos x-4\cos^3x)$
Pt đã cho $\Leftrightarrow 8(\sin x+\cos x)-4(\sin x+\cos x)(1-\sin x\cos x)=2\sqrt{2} (2+\sin 2x)$
$\Leftrightarrow 4(\sin x+\cos x)(1+\sin x\cos x)=2\sqrt{2} (2+\sin 2x)$
$\Leftrightarrow (\sin x+\cos x)(2+\sin 2x)=\sqrt{2}(2+\sin 2x) $
$\Leftrightarrow (2+\sin 2x)(\sqrt{2}\sin(x+\frac{\pi}{4})-\sqrt{2})=0 $
$\Leftrightarrow \left[ {\begin{matrix} \sin 2x=-2(l)\\ \sin(x+\frac{\pi}{4})=1 \end{matrix}} \right.$
$\Leftrightarrow x=\frac{\pi}{4}+k2\pi;k\in Z$