(a)[3]
By expanding $\cos(2\theta + \theta)$ first, prove that $\cos 3\theta = 4\cos^3 \theta - 3\cos \theta$.
(b)[2]
Determine the exact value of $2\cos^3\left(\frac{5\pi}{18}\right) - \frac{3}{2}\cos\left(\frac{5\pi}{18}\right)$.
(c)[4]
Find $\int (12\cos^3 x - 4\cos^3 3x)\,dx$.