I've drawn a picture and I think I know what the method is:Let be distinct points, and angles such that .
Let OPQO' be a quadrilateral such that , are directed angles (both clockwise as interior angles), and PQ halves both. Find the unique point for which .
So the next step was to equate the two and solve it for values of and .
However, this is really long!!
Is there a shorter way to do this?