Let M = [[sin⁴θ, −1 − sin²θ], [1 + cos²θ, cos⁴θ]] = 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 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