Take Your Time

As I surmised, the fat-soluble THC and associated cannabinoids can be released into the body more quickly with serious fasting. It is not advised to fast according to Marijuana Anonymous®  https://www.marijuana-anonymous.org/literature/pamphlets/detoxing-from-marijuana

As far as eating is concerned, I expect you will have to eat during the period of time it takes to eliminate cannabinoids from your body. Just because a urine test can detect use for approximately one month after having used doesn't mean that all traces are eliminated from your system in one month. There are more sensitive blood, saliva, and hair assays that can determine the continued presence of cannabinoids. You're not going to go without eating for three months, obviously. 

The answer is to stop all intake of cannabis - period. With time, your cells will eventually rid themselves of their THC content. Remember, your brain cells also contain these unwanted molecules, and all the fasting and exercise is not going to speed up the elimination from those cells. Juice fasts may cleanse your colon, but not your brain.