\(
\eqalign{
& a + b + c = \pi \cr
& a + b = \pi - c \cr
& \tan \left( {a + b} \right) = \tan \left( {\pi - c} \right) \cr
& \frac{{\tan (a) + \tan (b)}}
{{1 - \tan (a)\tan (b)}} = - \tan (c) \cr
& \tan (a) + \tan (b) = - \tan (c)\left( {1 - \tan (a)\tan (b)} \right) \cr
& \tan (a) + \tan (b) = - \tan (c) + \tan (a)\tan (b)\tan (c) \cr
& \tan (a) + \tan (b) + \tan (c) = \tan (a)\tan (b)\tan (c) \cr}
\)
