(c) $\tan \,\,{9^o} – \tan \,\,{27^o} – \tan \,\,{63^o} + \tan \,\,{81^o}$

$ = \tan \,\,{9^o} – \tan \,\,{27^o} – \cot \,\,{27^o} + \cot \,\,{9^o}$

$ = (\tan \,\,{9^o} + \cot \,\,{9^o}) – (\tan \,\,{27^o} + \cot \,\,{27^o})$

$ = \frac{{\cos ({9^o} – {9^o})}}{{\sin {9^o}\cos {9^o}}} – \frac{{\cos ({{27}^o} – {{27}^o})}}{{\sin {{27}^o}.\cos {{27}^o}}} = \frac{2}{{\sin {{18}^o}}} – \frac{2}{{\sin {{54}^o}}}$

$ = 2\,\left\{ {\frac{{\sin \,\,{{54}^o} – \sin \,\,{{18}^o}}}{{\sin \,\,{{18}^o}\,\sin \,\,{{54}^o}}}} \right\} $

$= 2.\,\,\frac{{2\,.\,\cos \,\,{{36}^o}.\,\sin \,\,{{18}^o}}}{{\sin \,\,{{18}^o}.\,\sin \,\,{{54}^o}}} = 4$