$PT\Leftrightarrow\frac{1+\cos
2x}{2}+\sqrt{2}\sin 2x+1=0\Leftrightarrow \cos 2x+2\sqrt{2}\sin 2x=-3$
Đặt $\cos\alpha=\frac{1}{3}\Rightarrow\sin\alpha=\frac{2\sqrt{2}}{3}$
$PT\Leftrightarrow\cos(2x-\alpha)=-1\Leftrightarrow
2x-\alpha=\pi+k2\pi$
$\Leftrightarrow
x=\frac{\alpha}{2}+\frac{\pi}{2}+k\pi, k\in Z$