(i)[3]
Show that $\sin(\theta + 60^{\circ}) + \sin(\theta + 120^{\circ})$ is equal to $(\sqrt{3})\cos \theta$.
(ii(a))[2]
Find the exact value for $\sin 105^{\circ} + \sin 165^{\circ}$.
(ii(b))[3]
Solve for $\theta$ in $0^{\circ} \leq \theta \leq 180^{\circ}$: $\sin(\theta + 60^{\circ}) + \sin(\theta + 120^{\circ}) = \sec \theta$.