Obtain a confidence set for with confidence coefficient 1

Question

Let X₁, ..., X_n be i.i.d. from N(µ, σ²).

(a) Suppose that σ² = γµ² with unknown γ > 0 and µ ∈ R. Obtain a confidence set for γ with confidence coefficient 1 - α by inverting the acceptance regions of LR tests for H₀; γ = γ₀ versus H₁; γ ≠ γ₀.

(b) Repeat (a) when σ² = γµ with unknown γ > 0 and µ > 0.