If you were on a first date, would you disclose that all the other girls you had asked before had turned you down?
School know that you're a reapplicant. I don't feel that being a 2nd vs 3rd time reapplicant makes that big a difference in showing your determination. Most of your peers (competitors at this point) are determined and interested in dentistry.
IMHO, highlighting the fact that you're a 3rd time reapplicant accentuates your flaws. If I was an adcom, I'd wonder what's wrong with you that no school accepted you the first two times. I'd be reluctant to accept a student that my peers have all ignored.
You shouldn't draw attention to a blemish, whether it be a bad grade or failure to get accepted to a school. If asked, you 're best bet is to redirect the conversation to how you improved between cycles.