I was about to post this as a "How-do-I" question, but while composing my question, I stumbled upon the solution.  In case this "discovery" would be useful, I'm posting it here.

For some coursework, I'm developing fitting sinusoids to experimental data (poor-man's Fourier Analysis).  At one point, I do a "brute-force-least-squares" computation, one step of which involves computing the sum of a sine over N equally-spaced intervals around the circle.  This sum is easily expressed in Maple as sum(sin(2*Pi*i/N), i = 1 .. N), but when you ask Maple to evaluate it, you get a messy expression, not the expected answer of 0.  Similarly, when you try to sum the square of the sinusoid, you get a messier expression instead of N/2.

The trick is to right-click the expression and choose "simplify trig".  This gives the expected results of 0 and N/2.  Problem solved!

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