VWO 2006 Problem 1

(a) Solve for $\theta\in\mathbb{R}$ : $\cos(4\theta) = \cos(3\theta)$

(b) $\cos\left(\frac{2\pi}{7}\right)$ , $\cos\left(\frac{4\pi}{7}\right)$ and $\cos\left(\frac{6\pi}{7}\right)$ are the roots of an equation of the form $ax^3+bx^2+cx+d = 0$ where $a, b, c, d$ are integers. Determine $a, b, c$ and $d$ .