`(2sin x + 1)(sin 2x + 1) = 3 - 4cos^2 x`
`<=> (2sin x + 1)(sin 2x + 1) = 3 - 4 + 4sin^2 x`
`<=> (2sin x + 1)(sin 2x + 1) = (2sin x)^2 - 1`
`<=> (2sin x + 1)(sin 2x + 1) = (2sin x - 1)(2sin x + 1)`
`<=> (2sin x + 1)(sin 2x + 1) - (2sin x - 1)(2sin x + 1) = 0`
`<=> (2sin x + 1)(sin 2x + 1 - 2sin x - 1) = 0`
`<=> (2sin x + 1)(sin 2x - 2sin x)= 0`
`<=> (2sin x + 1).sin x(2cos x - 2) = 0`
`<=>` \(\left[ \begin{array}{l}2sin x + 1 = 0\\sin x = 0\\2cos x - 2 = 0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}sin x = -\dfrac{1}{2}\\x = kπ\\cos x = 1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x = -\dfrac{π}{6} + k2π\\x = \dfrac{7π}{6} + k2π\\x = kπ\\x = k2π\end{array} \right.\) `(k ∈ ZZ)`
