If $$A = \begin{bmatrix} 1 & \sin\theta & 1 \\ -\sin\theta & 1 & \sin\theta \\ -1 & -\sin\theta & 1 \end{bmatrix}$$, then for all $$\theta \in \left(\frac{3\pi}{4}, \frac{5\pi}{4}\right)$$, det(A) lies in the interval:

A

$$\left(1, \frac{5}{2}\right]$$

B

$$\left[\frac{5}{2}, 4\right)$$

C

$$\left(\frac{3}{2}, 3\right]$$

D

$$\left(0, \frac{3}{2}\right]$$