`sin2x +2cosx = 1 + sin4x - 4cosx`
`->2sinxcosx+2(2cos^2x-1)-1-sinx+4cosx=0`
`->sinx(2cosx-1)+4cos^2x+4cosx-3=0`
`->sinx(2cosx-1)+(2cosx-1)(2cosx+3)=0`
`->(2cosx-1)(2sinx+2cosx+3)=0`
`->`\(\left[ \begin{array}{l}cosx=\frac{1}{2}\\2sinx+2cosx=-3\end{array}
\right.\)
`->x=+-frac{pi}{3}+k2\pi`