To find the angle of slipping of a falling coin

In an attempt to predict the outcome of a toss, I dropped a coin with its edge just touching another sharp edge as shown in figure. (The edge is flat and sharp with very less friction as in case of a blade)

I expected the calculations to be simple but it doesn’t seem so.
The main issue is in finding the angle at which it slips and start falling freely.
Had gravity been a bit weak, I could have experimented but now I think I have to theorise it.

I would like to know the angle at which the coin would fall. If that is a wrong question to ask, then please explain how to find the angular velocity of coin during free fall.