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