It's about preparation. Approximate gut motility for a healthy adult on a light diet is about 48-60 hours. So, stop eating 3 days before you leave, poop out all you possibly can before your 3 day period starts. Drink about 500ml water per day in the days leading up to the 3 day period. It wouldn't hurt to prep with a mild laxative to remove as much gut content as possible.
Once the timer starts, start eating small amounts only after the first day. For water, about 500ml per day. The good news is that what you pee out can't take much more space than the fresh water you drink.
This assumes you are relatively sedentary. If you perform manual labor during the 3 day period, you'll need to increase water intake, and possibly food intake, to avoid exhaustion.