Question 7 - A-Level Maths

\includegraphics[max width=\textwidth, alt={}, center]{5201a3d5-7733-4d10-9de5-0c2255e3ad60-12_499_568_267_826} The diagram shows part of the graph of $y = a + b \sin x$. Find the values of the constants $a$ and $b$.
1. Show that the equation $$( \sin \theta + 2 \cos \theta ) ( 1 + \sin \theta - \cos \theta ) = \sin \theta ( 1 + \cos \theta )$$ may be expressed as $3 \cos ^ { 2 } \theta - 2 \cos \theta - 1 = 0$.
2. Hence solve the equation $$( \sin \theta + 2 \cos \theta ) ( 1 + \sin \theta - \cos \theta ) = \sin \theta ( 1 + \cos \theta )$$ for $- 180 ^ { \circ } \leqslant \theta \leqslant 180 ^ { \circ }$.