\(\Leftrightarrow sin3x+cos3x+8\sqrt{2}sin^2x-2sinx=2\sqrt{2}\)
\(\Leftrightarrow sinx-4sin^3x+8\sqrt{2}sin^2x-2\sqrt{2}+4cos^3x-3cosx=0\)
\(\Leftrightarrow sinx\left(1-4sin^2x\right)-2\sqrt{2}\left(1-4sin^2x\right)+cosx\left(4cos^2x-3\right)=0\)
\(\Leftrightarrow\left(sinx-2\sqrt{2}\right)\left(1-4sin^2x\right)+cosx\left(4-4sin^2x-3\right)=0\)
\(\Leftrightarrow\left(sinx-2\sqrt{2}\right)\left(1-4sin^2x\right)+cosx\left(1-4sin^2x\right)=0\)
\(\Leftrightarrow\left(sinx+cosx-2\sqrt{2}\right)\left(1-4sin^2x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx+cosx=2\sqrt{2}\\2-4sin^2x=1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}sin\left(x+\frac{\pi}{4}\right)=2\left(vn\right)\\2cos2x=1\end{matrix}\right.\)
\(\Rightarrow cos2x=\frac{1}{2}\)
\(\Rightarrow x=...\)
