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[itex]\oint[/itex]1/(3-sinθ) by transforming to a complex contour, which enloses the origin, and then using the residue theorem. Normally you would transform to the unit circle, but in principal you could use any contour (right?). Now, sometimes you find that some rediues are inside the unit circle and some are not. If you picked a difference contour this could be changed. However, the integral above must give the same for every contour, so what is it that still makes the complex integrals give the same (even though different contours are involved.)