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If \( A^{-1}=\left[\begin{array}{ccc}\sin ^{2} \alpha & 0 & 0 \\ 0 & \sin ^{2} \beta & 0 \\ 0 & 0 & \sin ^{2} \gamma\end{array}\right] \) and \( B^{-1}=\left[\begin{array}{ccc}\cos ^{2} \alpha & 0 & 0 \\ 0 & \cos ^{2} \beta & 0 \\ 0 & 0 & \cos ^{2} \gamma\end{array}\right] \) where \( \alpha, \beta, \gamma \) real numbers and \( C=\left(A^{-5}+B^{-5}\right)+5 A^{-1} B^{-1}\left(A^{-3}+B^{-3}\right) \) \( +10 A^{-2} B^{-2}\left(A^{-1}+B^{-1}\right) \) then find \( |C| \).
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