Question 4 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2008
Session	June
Topic	Addition & Double Angle Formulae

Show that the equation $\tan \left( 30 ^ { \circ } + \theta \right) = 2 \tan \left( 60 ^ { \circ } - \theta \right)$ can be written in the form $$\tan ^ { 2 } \theta + ( 6 \sqrt { } 3 ) \tan \theta - 5 = 0$$
Hence, or otherwise, solve the equation $$\tan \left( 30 ^ { \circ } + \theta \right) = 2 \tan \left( 60 ^ { \circ } - \theta \right) ,$$ for $0 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }$.