\(\Leftrightarrow\left(2sinx-1\right)\left(2cos2x+2sinx+3\right)-\left(2sinx-1\right)\left(2sinx+1\right)=0\)
\(\Leftrightarrow\left(2sinx-1\right)\left(2cos2x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}sinx=\dfrac{1}{2}\\cos2x=-1\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{\pi}{6}+k2\pi\\x=\dfrac{5\pi}{6}+k2\pi\\x=\dfrac{\pi}{2}+k\pi\end{matrix}\right.\)
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