Explanation

(b)
$\cos\frac{\pi}{15}.\cos{\frac{2\pi}{15}.\cos\frac{4\pi}{15}.\cos\frac{8\pi}{15}}$
$= \frac{1}{4}\left( 2\cos{\frac{4\pi}{15}\cos\frac{\pi}{15}} \right)\left( 2\cos{\frac{8\pi}{15}\cos\frac{2\pi}{15}} \right)$
$= \frac{1}{4}\left( \cos{60{^\circ} + \cos{36{^\circ}}} \right)(\cos{120{^\circ} + \cos{72{^\circ}}})$
$= \frac{1}{4}\left( \frac{1}{2} + \frac{\sqrt{5} + 1}{4} \right)\left( - \frac{1}{2} + \frac{\sqrt{5} - 1}{4} \right)$
$= \frac{1}{4}\left\lbrack - \frac{1}{4} + \frac{1}{2}\left( \frac{\sqrt{5} - 1}{4} - \frac{\sqrt{5} + 1}{4} \right) + \frac{5 - 1}{16} \right\rbrack = - \frac{1}{16}$