Matrices and Determinants

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