I hope someone can answer, θ∈ R, z = (a + cos θ) + (2A - sin θ) I If the modulus of complex z = (a + cos θ) + (2A - sin θ) I does not exceed 2 for all θ∈ R, then the value range of real number a is_______ .

I hope someone can answer, θ∈ R, z = (a + cos θ) + (2A - sin θ) I If the modulus of complex z = (a + cos θ) + (2A - sin θ) I does not exceed 2 for all θ∈ R, then the value range of real number a is_______ .

|Z | = √ [(a + cos θ) ^ 2 + (2A - sin θ) ^ 2] = √ (5a ^ 2 + 1 + 2acos θ - 4asin θ) = {5A ^ 2 + 1 + √ [(2a) ^ 2 + 4A ^ 2)] * sin (θ + α)} = √ [5A ^ 2 + 1 + 2 √ 5A * sin (θ + α)] the value of α is determined by A|