(i) By expanding \(\sin(2\theta + \theta)\), demonstrate that \(\sin 3\theta = 3 \sin \theta - 4 \sin^3 \theta\).

(ii) Prove that, using the substitution \(x = \frac{2 \sin \theta}{\sqrt{3}}\), the equation \(x^3 - x + \frac{1}{6}\sqrt{3} = 0\) can be rewritten in the form \(\sin 3\theta = \frac{3}{4}\).

(iii) Solve the equation \(x^3 - x + \frac{1}{6}\sqrt{3} = 0\), providing answers to three significant figures.