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.