(a) Verify the identity \((2x - 1)(4x^2 + 2x - 1) \equiv 8x^3 - 4x + 1\).

(b) Prove the identity \(\frac{\tan^2 \theta + 1}{\tan^2 \theta - 1} \equiv \frac{1}{1 - 2 \cos^2 \theta}\).

(c) Using the results of (a) and (b), solve the equation \(\frac{\tan^2 \theta + 1}{\tan^2 \theta - 1} = 4 \cos \theta\), for \(0^\circ \leq \theta \leq 180^\circ\).