Be that as it may there has been much speculation as to the best times to use ToC.
As far as I can tell fire teams of three have the best luck when everyone uses a coin on the third ultra kill.
Best way to do this is to use a coin and kill an ultra to get your count to zero. Then complete two strikes without a coin use and on the third strike use a ToC before the boss.
This technique has worked well for some and terribly for others. Personally I think you should just play the game and use a Three of Coins whenever you remember.
Be safe guardians