(i) By expanding \((\cos^2 x + \sin^2 x)^3\), or using another method, demonstrate that \(\cos^6 x + \sin^6 x = 1 - \frac{3}{4} \sin^2 2x\).

(ii) Solve the equation \(\cos^6 x + \sin^6 x = \frac{2}{3}\) for \(0^\circ < x < 180^\circ\).