As you already know, there are no exact angles attributed to CTE. It depends on the shot and the perception you use. For every shot and every perception there are only 2 angles (thicker or thinner than the perception) that can be created if you perform the half tip manual pivot as described/defined. If one of these puts you on the shot line then it'll work, like magic. But if it's off a touch, it won't work unless you have the experience needed to make it work.
For an example, roll the cb and ob across the table and wherever they stop that'll be our shot. Use whatever perception you think the shot requires, a 15, 30, whatever.... If you are were a beginning CTE user, just trying to follow precise instructions, doing a manual pivot may or may not put you on the shot line. If it happens to work out then the ball will go into the pocket. If it doesn't just happen to work out then the ball will miss the pocket. The exact angle is not important. Recognizing that a 15-inside is dead on or a little off is important. With enough practice you begin to recognize this much easier, and you begin to learn how to make it work when that 15-inside looks just a touch off. You, being a veteran CTE user, would just call it a 15-inside and fire it in, automatically making whatever fine tuning might or might not be needed due to your experience with the system.