I'm going to be the dissenting voice here - the 70-200 can be more than enough. It depends largely on where you go though. I was in Sanbona, South Africa last year and I rarely felt limited by 200mm. Just to give a few examples
Of course there was occasions where 200mm wasn't enough to give a closeup, but that will be true of any focal length:
In the end I liked the environmental portraits of the animals much better than the close ups. If you want an awesome closeup of a lion's head, just google "lion" and you'll get a ton of images. People have been photographing lions for a long time and there are some really good shots available. No point in replicating that. Instead it's much more interesting to photograph the animal in the context of it's natural environment.
My first advice would hence be - don't forget to bring a wide angle!