Mind Over Matter+Betrayal

[Cavius The Great]

Can I continuously tap one of my opponent's creatures enchanted with Betrayal with Mind Over Matter to draw my entire deck? Or does it have to be untapped for me to actually tap the creature? Plz let me know. Thanx ahead of time, Peace.

[Nihil Credo]

You can tap an already tapped creature, but doing so doesn't make it "become tapped", and therefore Betrayal won't trigger.