Let M= [ array cc ^ 4 & -1- ^ 2 1+ ^ 2 & ^ 4 array ]= I+ M^ -1 where α = α(θ) and β =…

Let \[M=\left[\begin{array}{cc} \sin ^{4} \theta & -1-\sin ^{2} \theta \\ 1+\cos ^{2} \theta & \cos ^{4} \theta \end{array}\right]=\alpha I+\beta M^{-1}\]
where α = α(θ) and β = β(θ) are real numbers, and I is the 2 × 2 identity matrix.
If α* is the minimum of the set {α(θ) : θ ∈[0, 2π)} and
β* is the minimum of the set {β(θ) : θ ∈ [0, 2π)},
then the value of α* + β* is