Russ,
One way or another, you are "solving" in along he path of an asymptotic function. And no CAS will do better than another one, no maths either. A similar situation exists in one of those "free fall" equations. In that last problem that kept me busy several days, I had reached the same limit value found in books, but no further. No matter the epsilon or whatever else, it wouldn't go further. The system is self limiting, as simple as that. Where does it saturates ? Don't know, just the physics of the system. If there is a way to locate ? Don't think so either. The Theta limiting value moves a bit by playing with Alpha.
Teachers love those kind of quiz, they worth points !
jmG