Let $$M = \left[ \begin{array} { c c } \sin ^ { 4 } \theta & - 1 - \sin ^ { 2 } \theta \\ 1 + \cos ^ { 2 } \theta & \cos ^ { 4 } \theta \end{array} \right] = \alpha I + \beta M ^ { - 1 }$$ where $\alpha = \alpha ( \theta )$ and $\beta = \beta ( \theta )$ are real numbers, and $I$ is the $2 \times 2$ identity matrix. If $\alpha ^ { * }$ is the minimum of the set $\{ \alpha ( \theta ) : \theta \in [ 0,2 \pi ) \}$ and $\beta ^ { * }$ is the minimum of the set $\{ \beta ( \theta ) : \theta \in [ 0,2 \pi ) \}$, then the value of $\alpha ^ { * } + \beta ^ { * }$ is
(A) $- \frac { 37 } { 16 }$
(B) $- \frac { 31 } { 16 }$
(C) $- \frac { 29 } { 16 }$
(D) $- \frac { 17 } { 16 }$