Let $\mathrm{M}=\left[\begin{array}{cc}{\sin }^4\mathrm{\theta }& -1-{\sin }^2\mathrm{\theta }\\ 1+{\cos }^2\mathrm{\theta }& {\cos }^4\mathrm{\theta }\end{array}\right]=\mathrm{\alpha I}+{\mathrm{\beta M}}^{-1}$  where $\mathrm{\alpha }=\mathrm{\alpha }\left(\mathrm{\theta }\right)\text{ and }\mathrm{\beta }=\mathrm{\beta }\left(\mathrm{\theta }\right)$ are real numbers, and I is the 2x2 identity matrix. If  

${\mathrm{\alpha }}^{\ast }$ is the minimum of the set $\left\{\mathrm{\alpha }\right(\mathrm{\theta }):\mathrm{\theta }\in [0,2\mathrm{\pi }\left)\right\}$ and

${\mathrm{\beta }}^{\ast }$ is the minimum of the set $\left\{\mathrm{\beta }\right(\mathrm{\theta }):\mathrm{\theta }\in [0,2\mathrm{\pi }\left)\right\}$, 
then the value of ${\mathrm{\alpha }}^{\ast }+{\mathrm{\beta }}^{\ast }$ is