\(ABCDE\) is a regular pentagon. By projecting the broken line \(AED\) on the line \(AB\), or otherwise, show that \[\cos\dfrac{\pi}{5}-\cos\dfrac{2\pi}{5}=\frac{1}{2}.\]

Hence, or otherwise, show that \(\cos\dfrac{\pi}{5} = \dfrac{\sqrt{5}+1}{4}\).

Show further that \(\cos\dfrac{3\pi}{5} = -\dfrac{\sqrt{5}-1}{4}\).