Let $d\in\mathbb{R}$, and $A=\begin{bmatrix} -2 & 4+d & \sin\theta-2\\ 1 & \sin\theta+2 & d\\ 5 & 2\sin\theta-d & -\sin\theta+2+2d \end{bmatrix},\ \theta\in[0,2\pi].$ If the minimum value of $\det(A)$ is $8$, then a value of $d$ is: