1. (i) On the same set of axes, sketch the graphs of $y=tan\frac{1}{4} \theta$ and $y=cos( \theta +120^{\circ})$ in the interval $0^{\circ}\leq \theta \leq270^{\circ}$. Show clearly the coordinates of all points of intersection with the coordinate axes.

(ii) Deduce the number of solutions to the equation $cos( \theta +120^{\circ})-tan\frac{1}{4} \theta =0$, in the interval $0^{\circ}\leq \theta \leq270^{\circ}$.