If VAPA1 = (Tan PA1) - (Arc PA1) = INVPA1
The AGMA "Manual of Gear Design" book descibes this as a "vectorial angle".
The book gives an example:
VAPA1 = (Tan 14.5°) - ((PI/180) * 14.5°) = .00554
INVPA1 = .00554
If I have INVPA2 = .057897
I need to find PA2
,which is what your equation is - where is an angle measured in radians, and is a constant.
The best you can do is to use a numerical method to get an approximation to the answer. As I said, I used Excel, which has a Goal Seek facility. This usually enables you to get an accurate answer to a problem like this very quickly - although in this case, the answer wasn't very accurate, so I refined it manually, using basically a 'trial and error' process to home in on the answer.
It sounds a bit unsatisfactory, but it's actually very quick and easy to do.