Let M=[sin4θ−1−sin2θ1+cos2θcos4θ]=αI+βM−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 set {α(θ):θ∈[0,2π)} and β∗ is the minimum of set {β(θ):θ∈[0,2π]}, then the value of α∗+β∗ is

Let M=[sin4θ−1−sin2θ1+cos2θcos4θ]=αI+βM−1,Where α=α(θ)

1.	Let M=[sin4θ−1−sin2θ1+cos2θcos4θ]=αI+βM−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 set {α(θ):θ∈[0,2π)} and β∗ is the minimum of set {β(θ):θ∈[0,2π]}, then the value of α∗+β∗ is
Answer» $L e t M = [\begin{matrix} {sin}^{4} θ & - 1 - {sin}^{2} θ 1 + {cos}^{2} θ & {cos}^{4} θ \end{matrix}] = α I + β M^{- 1},$ Where $α = α (θ) a n d β = β (θ)$ are real numbers, and $I$ is the $2 \times 2$ identity matrix. If $α^{}$ is the minimum of set ${α (θ) : θ \in [0, 2 π)}$ and $β^{}$ is the minimum of set ${β (θ) : θ \in [0, 2 π]}$ , then the value of $α^{}$ + $β^{}$ is