Complex sentence: The fickle Duke courts Olivette, thinking that she is the Countess and boasts of his success so loudly that both the Captain and Valentine disown Olivette until she is able to prove an alibi.
Split into simpler sentences: The fickle Duke courts Olivette, thinking that she is the Countess. The Duke boasts of his success so loudly that both the Captain and Valentine disown Olivette until she is able to prove an alibi.