4. In this question you should show detailed reasoning.
\section*{Solutions relying entirely on calculator technology are not acceptable.}
- Show that the equation
$$2 \sin \left( \theta - 30 ^ { \circ } \right) = 5 \cos \theta$$
can be written in the form
$$\tan \theta = 2 \sqrt { 3 }$$
- Hence, or otherwise, solve for \(0 \leqslant x \leqslant 360 ^ { \circ }\)
$$2 \sin \left( x - 10 ^ { \circ } \right) = 5 \cos \left( x + 20 ^ { \circ } \right)$$
giving your answers to one decimal place.