I've been keeping this tab open on my browser because I wanted to work out the solution myself. I finally figured it out (2 years later). Don't give in and look at the solution without giving it a good try. Hint, you can do it without any trigonometric functions and without Pythagoras' help.
This is known as Langley's Adventitious Angles. And a good visual solution can be seen here (warning Flash required).
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