Hello rampman,
Before the push, ask the crew,should be in the Aircraft Operation manual of the airline (Limitations chapter) if there is a limit.
Now, I would expect that for the ramp guys, the limits is the red line on the NLG doors. It is unrealistic to expect from you to know the limits for every aircraft/operator on the apron.
For your info, my company (but I asuume it is manufacturer limits) are:
A330/A340 :
Nose wheel steering : max. :72°
Towing : max.65° or red marks