vx
Phosphoric acid like Pioneer said. Softens the stones. It's like ultraphos+apple juice.
The second reason is to make it easier to drink. It sounds like a stupid reason to add it, but if people either can't drink the OO or if people dislike the liver flush so much they don't do that, it makes the procedure useless right? Personally, I had trouble downing the OO after flush 7, my body would just reject it immediately. A little coke and voila, I'm at flush #17 with no problems.
To me, it's only 2 ounces of coke (non-diet), it's a very small amount (it's not even half of these tiny little baby bottles I have) and it's not like I'm drinking it every day.
It's your choice, if you can drink the OO without, go for it. The original Clark flush works fine.