8. (a) Starting from the formulae for \(\sin ( A + B )\) and \(\cos ( A + B )\), prove that
(b) Deduce that $$\tan ( A + B ) = \frac { \tan A + \tan B } { 1 - \tan A \tan B }$$ (c) Hence, or otherwise, solve, for \(0 \leqslant \theta \leqslant \pi\), $$\tan \left( \theta + \frac { \pi } { 6 } \right) = \frac { 1 + \sqrt { } 3 \tan \theta } { \sqrt { } 3 - \tan \theta }$$ (c) Hence, or otherwise, solve, for \(0 \leqslant \theta \leqslant \pi\),
(c) $$1 + \sqrt { } 3 \tan \theta = ( \sqrt { } 3 - \tan \theta ) \tan ( \pi - \theta )$$ \section*{}