Explanation

(a)
$\sin{\frac{\pi}{16}.\sin{\frac{3\pi}{16}.\sin{\frac{5\pi}{16}.\sin\frac{7\pi}{16}}}}$
$= \frac{1}{2}\left\lbrack 2\sin{\frac{5\pi}{16}\sin\frac{3\pi}{16}} \right\rbrack \times \frac{1}{2}\left\lbrack 2\sin{\frac{7\pi}{16}\sin\frac{\pi}{16}} \right\rbrack$
$= \frac{1}{4}\left\lbrack \left( \cos{\frac{\pi}{8} - \cos\frac{\pi}{2}} \right)\left( \cos{\frac{3\pi}{8} - \cos\frac{\pi}{2}} \right) \right\rbrack$
$= \frac{1}{4 \times 2}\left( \cos{\frac{\pi}{2} + \cos\frac{\pi}{4}} \right)$
$= \frac{1}{8\sqrt{2}} = \frac{\sqrt{2}}{16}$ $\left\lbrack \because\cos{\frac{\pi}{2} = 0} \right\rbrack$