Let $$M = \left[ {\begin{matrix} {{{\sin }^4}\theta } \\ {1 + {{\cos }^2}\theta } \\ \end{matrix} \begin{matrix} { - 1 - {{\sin }^2}\theta } \\ {{{\cos }^4}\theta } \\ \end{matrix} } \right] = \alpha I + \beta {M^{ - 1}}$$, 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 {$\beta$($\theta$) : $\theta \in$ [0, 2 $\pi${)}, then the value of $\alpha$* + $\beta$* is