How do Freddie and Anne-Marie become close throughout the performance?

Anne-Marie and Freddie sit together before the play begins, but once Freddie is seized and hooded, then sequestered in a lone cell, Anne-Marie finds him and tells him what he will need to do to survive. She tells him the prison is being taken over by a mad man and that they need to play along with his production of the Tempest. She brings the script of the Tempest, and teaches him his lines, and in the process of rehearsing together, the two of them fall in love.