Question 3 - A-Level Maths

Exam Board	CAIE
Module	P3 (Pure Mathematics 3)
Year	2019
Session	March
Topic	Addition & Double Angle Formulae

Given that \(\sin \left( \theta + 45 ^ { \circ } \right) + 2 \cos \left( \theta + 60 ^ { \circ } \right) = 3 \cos \theta\), find the exact value of \(\tan \theta\) in a form involving surds. You need not simplify your answer.
Hence solve the equation \(\sin \left( \theta + 45 ^ { \circ } \right) + 2 \cos \left( \theta + 60 ^ { \circ } \right) = 3 \cos \theta\) for \(0 ^ { \circ } < \theta < 360 ^ { \circ }\).