If \( 2 \sin^{3} x + \sin 2x \cos x + 4 \sin x - 4 = 0 \) has exactly \( 3 \) solutions in the interval \( \left[ 0, \dfrac{n\pi}{2} \right], \; n \in \mathbb{N} \), then the roots of the equation \( x^{2} + nx + (n - 3) = 0 \) belong to:
\( (0, \infty) \)
\( \left( -\dfrac{\sqrt{17}}{2}, \dfrac{\sqrt{17}}{2} \right) \)
\( \mathbb{Z} \)
\( (-\infty, 0) \)
