Phew is longer than 1/2 outer base lines
Which means there is no way for it to be correct.
What makes phew be powerful in tiny angles is, phew AKA 1/2 C reflects a pure arc
No it doesn't,
Your number has no connection to an arc at all. Instead you just try to deal with large straight lines and pretend that should resemble an arc for some reason.
Meanwhile, Pi's approximation of an arc actually approximates it, rather than getting it horribly wrong like phew does.
And inner base lines, even outer base lines, will be shorter than the arcs
Again, it is physically impossible for the arc to be longer than the outer base line.
I have proven the arc needs to be shorter.
If you wish to disagree you will need to prove it.
Jack forgot trigonometry. Try again 
You sure seem to love throwing out insults, yet have absolutely nothing of substance.
Do you know some basic trig?
Here is one for you:
sin(x)<x<tan(x), for x between 0 and pi/2.
i.e. the arc length lies between the chord and the tangents.
It seems you are the one that forgot it.