It's a monstrosity, no doubt, but there is a way. I'll outline it.

First I am assuming f is a constant, so I'll replace 1 + f with k for simplicity.

Get rid of the fraction. ie

Now expand the

Collect terms:

Now isolate the term and replace it with . Square both sides and collect like factors. You will now have a quadratic by which you can solve by the quadratic formula. Then take the inverse cosine of both sides.

I may/may not have some errors in there. But the basic method is still the same.

-Dan