It is well-known/well understood that the tilt of the axis does change, but not day to dfay or year to year...it is one of the Milankovitch cycles that partially controls ice ages/interglacial periods. I forget the period of this wobble, but it is probably 20,000 years or 40,000 years or something like that. And, I also forget the amount of change, but I think it is pretty large: ranging between about 15 and 25 degrees.
I could google the answers, but I'll let someone else do it..

Chris