Let $$ M=\left[\begin{array}{ccc} \sin ^4 \theta & -1-\sin ^2 \theta & \mid=\alpha I+\beta M \\ \left\lfloor\mid 1+\cos ^2 \theta\right. & \cos ^4 \theta & \mid\rfloor \end{array}\right. $$ where $\alpha=\alpha(\theta)$ and $\beta=\beta(\theta)$ are real number, 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