\(\Leftrightarrow\left(sin^2x-3cos^2x\right)+\left(\sqrt{6}cosx-\sqrt{2}sinx\right)=0\)
\(\Leftrightarrow\left(sinx-\sqrt{3}cosx\right)\left(sinx+\sqrt{3}cosx\right)-\sqrt{2}\left(sinx-\sqrt{3}cosx\right)=0\)
\(\Leftrightarrow\left(sinx-\sqrt{3}cosx\right)\left(sinx+\sqrt{3}cosx-\sqrt{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=\sqrt{3}cosx\\sinx+\sqrt{3}cosx=\sqrt{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}tanx=\sqrt{3}\\sin\left(x+\frac{\pi}{3}\right)=\frac{\sqrt{2}}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\frac{\pi}{3}+k\pi\\x+\frac{\pi}{3}=\frac{\pi}{4}+k2\pi\\x+\frac{\pi}{3}=\frac{3\pi}{4}+k2\pi\end{matrix}\right.\) \(\Leftrightarrow...\)
