Let \(d \in R\), and \(A = \left[ {\begin{array}{*{20}{c}}{ - 2}&{4 + d}&{\left( {{\rm{sin}}\theta } \right) - 2}\\1&{\left( {{\rm{sin}}\theta } \right) + 2}&d\\5&{\left( {2{\rm{sin}}\theta } \right) - d}&{\left( { - {\rm{sin}}\theta } \right) + 2 + 2d}\end{array}} \right]\), θ ∈ [0, 2π]. If the minimum value of det (A) is 8, then a value of d is:

Let \(d \in R\), and \(A = \left[ {\begin{array}{*{20}{c}}{ - 2}&{4

1.	Let \(d \in R\), and \(A = \left[ {\begin{array}{*{20}{c}}{ - 2}&{4 + d}&{\left( {{\rm{sin}}\theta } \right) - 2}\\1&{\left( {{\rm{sin}}\theta } \right) + 2}&d\\5&{\left( {2{\rm{sin}}\theta } \right) - d}&{\left( { - {\rm{sin}}\theta } \right) + 2 + 2d}\end{array}} \right]\), θ ∈ [0, 2π]. If the minimum value of det (A) is 8, then a value of d is:
A.	-5
B.	-7
C.	2(√2 + 1)
D.	2(√2 + 2)
Answer» B. -7