Explanation

(c)
$\sin{\frac{\pi}{5} + i\left( 1 - \cos\frac{\pi}{5} \right)}$
$= 2\sin{\frac{\pi}{10}.\cos{\frac{\pi}{10} + i\ 2\sin^{2}\frac{\pi}{10}}}\$
=2 sin $\frac{\pi}{10}\left( \cos{\frac{\pi}{10} + i\sin\frac{\pi}{10}} \right)\$
$\therefore\ \ \ \tan{\theta = \frac{\sin\frac{\pi}{10}}{\cos\frac{\pi}{10}} = \tan{\frac{\pi}{10}\ \ \ \ \Rightarrow \ \ \ \ \ }\theta = \frac{\pi}{10}}$