Let's figure out how to form a 15° arch
Let's not.
Let's instead discuss the derivation I provided.
It shows the value of pi, placing limits on it.
What point do you disagree with.
from its diagonal?
Only if you use an infinite series to converge to the arc by repeatedly breaking that arc into smaller and smaller lines. But you don't want that.
Are you kidding?? 
Again, you not liking how close the arc is to the diagonal just shows you don't like reality.
It doesn't magically make it wrong.
What you are doing is no better than claiming something like:
IT ONLY TAKES AN EXTRA 3.5 mm? THAT"S GARBAGE!! SURELY IT SHOULD TAKE AN EXTRA 10 M!!!
It is just pathetic, childish crap.
no bollock please
You provide enough bollock for everyone.
An example of that is this pile of crap:
What length should the diagonal get added to form a 15° arch?
Additional length = (Pi/4/3) - √[(sin30)²+(1-cos30)²]*100cm
Rather than writing it sensibly as pi/12, which is equivalent to 15 degrees, you instead stick in pi/4/3.
And rather than just leave it as a simple number, you felt the need to multiply by 100cm for no reason at all, but only showed you doing that to one side.
Let's skip that garbage shall we?
That means the arc length is (not just allegedly, but IS!) 0.26179938779
Then you tried computing the diagonal, but shoved in 30 degrees instead of 15. Why was that?
But then magically you still got the correct answer.
0.26105238444010
As a ratio, that is 0.997146657
You then claim more nonsense of that difference being clearly visible but it isn't.
To try and back this up you use an image where you aren't even drawing it in properly.
Here is what it should have looked like:

Not really any big difference is there?
Now which of the 60 points do you disagree with and why?
Unless you can show a problem with one of these points you have no argument and no justification for any of your nonsense.