There is a point $P$ in the first quadrant (not including the axes) at which the graph of $r=\cos(4\theta)+\sin(3\theta)$ for $\theta\in[0,2\pi]$ intersects itself. Find the angle that the ray from the origin to $P$ makes with the positive $x$-axis.
How would I go about solving this? I believe the point is around (0.8, 0.2), but I don't know the exact point. I also don't know how I would go about finding the angle it makes with the x-axis. Any answers/help would be appreciated.