Sineful mistake

Geometry Level 5

A common misconception of students is to claim that sinx+siny=sin[(x+y)], \sin x^\circ + \sin y^\circ = \sin [ (x+y)^ \circ], just because x+y=(x+y) x + y = (x+y) . There are NN ordered pairs of integers (x,y) (x, y) , each of which are between 0 and 360 (inclusive), which satisfy the equation sinx+siny=sin[(x+y)]. \sin x^\circ + \sin y^\circ = \sin [(x+y)^ \circ].

What are the last three digits of NN?

Details and assumptions

Notice that the equations are given in degrees, not radians.

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