2003 AIME I Problem 11

An angle x is chosen at random from the interval 0^\circ < x < 90^\circ. Let p be the probability that the numbers \sin^2 x, \cos^2 x, and \sin x \cos x are not the lengths of the sides of a triangle. Given that p = d/n, where d is the number of degrees in \arctan m and m and n are positive integers with m + n < 1000, find m + n.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.