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If $A = \begin{bmatrix} 1 & \sin\theta & 1 \ -\sin\theta & 1 & \sin\theta \ -1 & -\sin\theta & 1 \end{bmatrix}$; then for all $\theta \in \left(\dfrac{3\pi}{4}, \dfrac{5\pi}{4}\right)$, $\det(A)$ lies in the interval:
(1) $\left(1, \dfrac{5}{2}\right]$
(2) $\left[\dfrac{5}{2}, 4\right)$
(3) $\left(0, \dfrac{3}{2}\right]$
(4) $\left(\dfrac{3}{2}, 3\right]$
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