(a) Prove the identity \(\frac{1 - 2 \sin^2 \theta}{1 - \sin^2 \theta} \equiv 1 - \tan^2 \theta\).

(b) Hence solve the equation \(\frac{1 - 2 \sin^2 \theta}{1 - \sin^2 \theta} = 2 \tan^4 \theta\) for \(0^\circ \leq \theta \leq 180^\circ\).