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...