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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 ,
P then a value of \( d \) is :
(1) \( -5 \)
(2) \( 2(\sqrt{2}+2) \)
(3) \( 2(\sqrt{2}+1) \)
(4) \( -7 \)
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