Tính :tan9 độ -tan27 độ -tan63 độ +tan81 độ

$\begin{array}{l}
\tan \left( {{{90}^o} - a} \right) = \cot a\\
\tan {9^o} - \tan {27^o} - \tan {63^o} + \tan {81^o}\\
 = \tan {9^o} + \cot {9^o} - \left( {\tan {{27}^o} + \cot {{27}^o}} \right)\\
 = \dfrac{{\sin {9^o}}}{{\cos {9^o}}} + \dfrac{{\cos {9^o}}}{{\sin {9^o}}} - \left( {\dfrac{{\sin {{27}^o}}}{{\cos {{27}^o}}} + \dfrac{{\cos {{27}^o}}}{{\sin {{27}^o}}}} \right)\\
 = \dfrac{{{{\sin }^2}{9^o} + {{\cos }^2}{9^o}}}{{\cos {9^o}\sin {9^o}}} - \dfrac{{{{\sin }^2}{{27}^o} + {{\cos }^2}{{27}^o}}}{{\cos {{27}^o}\sin {{27}^o}}}\\
 = \dfrac{1}{{\cos {9^o}\sin {9^o}}} - \dfrac{1}{{\cos {{27}^o}\sin {{27}^o}}}\\
 = \dfrac{2}{{\sin {{18}^o}}} - \dfrac{2}{{\sin {{54}^o}}}\\
 = 2\left( {\dfrac{1}{{\sin {{18}^o}}} - \dfrac{1}{{\sin {{54}^o}}}} \right)\\
 = 2\left( {\dfrac{{\sin {{54}^o} - \sin {{18}^o}}}{{\sin {{18}^o}\sin {{54}^o}}}} \right)\\
 = \dfrac{{4\cos {{36}^o}\sin {{18}^o}}}{{\sin {{18}^o}\sin {{54}^o}}}\\
 = \dfrac{{4\cos {{36}^o}}}{{\sin {{54}^o}}} = 4
\end{array}$