Ah ha, but you guys are way over-thinking it.

It's not about funky angles or even math. It is simply flipping a circle from one direction to the other.

Draw 3 points on a wheel, A-B-C and then rotate that wheel (clockwise for example). No matter where you start, it will always be the same sequence: A-B-C, or B-C-A, or C-A-B. They are still in the same repeating sequence.

Then turn that wheel counterclockwise. The points are no longer in the same sequence. They become A-C-B, C-B-A, and B-A-C.

When you reverse any two conductors, you flip the direction of the sequence....regardless where your sequence started. Compare the two sequences below, and note that each column has the same starting letter, and you will see the differences.

A.B.C__B.C.A__C.A.B.........Clockwise

A.C.B.__B.A.C__C.B.A........Counterclockwise

Edit: Oh, who would have guessed Mivey was posting at the same time as me. Oops.