Previously we asked you, the educators or yourself, if you are a student to think of way(s) to find the ratio of $\dfrac{PR}{QR}$ in this thread (Olympiad Trigonometric Problem), we will now lead you to a credible way to solve for that intriguing hard trigonometric problem.
We in fact, should have the eagle eye sight and should be able to tell offhand that we suspect $\angle P=\angle Q$.