Hmm, the way I'm coming up with is pretty long.

Looking at the unit circle, you can define point P at and Q at . O is the origin. Then find the line perpendicular to line OQ going through P, call it line m. Find the intersection of m and OQ, call it point Z. Then verify that the length of line segement PZ divided by the length of line segment OZ is 2/3.

Someone care to share a better way?