Something else to keep in mind for future reference: Most people just sharpen the chamfer on the cutting end of a *straight* tap. That's easy -- you do it from the outside, not the inside of the gullets. They'll do that three or four times before going after the gullets.
But I try to sharpen them all the way up, because I do them by hand, and I'd rather keep them very sharp all the way along the edge so I never have much metal to remove.