Question 16
Determine the largest angle $\theta$ (in degree), where $0^\circ\le\theta\le360^\circ$, such that $$\sin(\theta+18^\circ)+\sin(\theta+162^\circ)+\sin(\theta+234^\circ)+\sin(\theta+306^\circ)$$ $$=1+\cos(\theta+60^\circ)+\cos(\theta+300^\circ).$$