How do you regain trust from a girl?

You better be a perfect angel and always be upfront. Don't hide your cell phone or take personal conversations out of the room so she can't hear. Don't disappear or ignore her calls. These types of thing create wonder and that creates doubt in her mind.

Answer: Most honest relationships start off with a state of trust - each person trusts the other.

Then either the players continue in a state of trust - neither betraying the other - or one betrays the other.

In the case that there is a betrayal, all the rules change. For their own protection the betrayed can never trust the other person again. Like the old saying "Fool me once - shame on you, fool me again - shate on me." Even if the betrayed party "Forgives and forgets", "Let's bygones be bygones." etc., the doubt is always there and will colour the relationshup.

This is covered by Games Theory in discussing the Prisoner's Dilemma. It sums up that the most advantageous course overall is trust, if that fails, burn the other player to the ground.