\(\Leftrightarrow1-2sin^2x+3sinx-2=0\)
\(\Leftrightarrow-2sin^2x+3sinx-1=0\)
\(\Rightarrow\left[{}\begin{matrix}sinx=1\\sinx=\frac{1}{2}\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}x=\frac{\pi}{2}+k2\pi\\x=\frac{\pi}{6}+k2\pi\\x=\frac{5\pi}{6}+k2\pi\end{matrix}\right.\)