JEE Math Practice Question

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

1. A.$$-$$ 7
2. B.$$2\left( {\sqrt 2 + 2} \right)$$
3. C.$$-$$ 5
4. D.$$2\left( {\sqrt 2 + 1} \right)$$