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

A

$$(0, \infty)$$

B

$$(-\infty, 0)$$

C

$$\left(-\frac{\sqrt{17}}{2}, \frac{\sqrt{17}}{2}\right)$$

D

$$\mathbb{Z}$$