\(2\left(1-cos^2x\right)+4cos^2x-cosx-3=0\)
\(\Leftrightarrow2cos^2x-cosx-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}cosx=1\\cosx=-\frac{1}{2}\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=k2\pi\\x=\pm\frac{2\pi}{3}+k2\pi\end{matrix}\right.\)