If \(2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0\) has exactly 3 solutions in the interval \(\left[0, \frac{ n \pi}{2}\righ…

If \(2 \sin ^3 x+\sin 2 x \cos x+4 \sin x-4=0\) has exactly 3 solutions in the interval \(\left[0, \frac{ n \pi}{2}\right], n \in N\), then the roots of the equation \(x^2+ n x+( n -3)=0\) belong to :

[JEE Main 2024, 30 Jan (Shift 1)]