There isn't any need to believe. The pool table sits there inert. The balls can be placed anywhere desired. The rails don't move, the pockets are stationary. The balls themselves don't move unless struck.
No one needs to take CTE on faith because everything needed to test it thoroughly is available to every pool player every where as long as they have access to a decent table and balls of equal size.
Again, angles don't matter. They don't. No aiming method refers to the angle of the shot and gives a formula to aim for it. Not a single one that I know of does this.
Why not?
Because no person can accurately say what the shot angle is consistently over any random ten shots. Can't do it, it's impossible. Oh some people can get closer than others but no person living can consistently do it shot after shot. So even speaking of angles, 25, 75, 180 whatever has zero bearing on the question of whether a system is objective or not. No one actively uses angles as part of their aiming process.
If they say they do then I want to hear about it and test them to see how accurately they can identify angles and then use that information to aim with. So honestly any such requirement that CTE "define" angles is merely a red herring in the discussion.
Even Ghost Ball makes no use of angles. Ghost Ball covers all angles but it doesn't define them. All you have to do is be able to accurately place a phantom ball at exactly the right size in exactly the right place shot after shot and then simply line up to replace it. Simple right? On paper it surely is.
So no, whereever you got this 75 angles thing from you can ship it back because no one thinks in angles when they play. Furthermore no angle has any bearing on any other angle. Once again each cue ball object ball relationship is a singular problem for which a solution (shot line) must be found and chosen.
Let me repeat that for the three people still reading, the shooter has to solve a single problem when facing each shot. He is not worried about the 75 degree angle shot when he is facing a 42 degree one. He needs a way to get to the shot line reliably for each shot he faces. In fact he doesn't even think in angles. The shooter thinks in terms of degrees of difficulty more than anything else.
And this is where CTE shines.
You asked
Easily. CTE has a single initial alignment, the center of the CB to the Edge of the OB. Two objective points that can be objectively connected visually. So the first step is to simply find the CTE Line clearly. The second step is to then find a second line which is the Edge of the Cueball lined up to one of the three defined aim points on the object ball, a-the first quarter division, b-the center of the CB or C-the third quarter division.
Once these two lines are firmly established, and it's pretty easy to do this the shooter then let's his eyes start out on one side and sweep over the ball with the cue stick moving with them until the cue stops at 1/2 tip away from center cue ball. The shooter then pivots into center ball and is on the shot line. The instructions are a little more detailed than that with inside and outside sweeps that thicken or thin the shot but those are also objective moves that don't change.
The shooter has zero need to be concerned with the actual cur angle as whatever it is CTE provides a solution for it since CTE starts at the cueball. And again all this bears out ON THE TABLE.
On the table is where all methods have to be worked out. This is how shooters determine the level of objectivity in a method and how reliable it is. CTE has proven itself to be 100% reliable.
