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The Tempest is a play the action of which is driven by rebellion and revolution.  Prospero is stranded on the island as a result of a plot between Antonio and Alonso to displace him in favor of his brother (I.ii.145 ff.).  On the island, Sebastian and Antonio plot of kill Alonso (II.i.332-6), and to make Sebastian the king of Naples, displacing his proper heir, Sebastian's sister Claribel.  Caliban recruits Stephano and Trinculo to kill Prospero and rule the island, with Stephano taking Miranda as his bride (III.ii.116-9).  Clearly, allegiance, duty, and the failure of both are themes in the play.

However, even though he was wrongly displaced by his "perfidious" brother, Prospero makes it clear that he lost his rule partly because of his own faults as a ruler, paying too much attention to his books, and too little to his government (I.ii.90-95).  So, while subjects owe allegiance to their ruler, it seems clear that rulers also owe a duty to their subjects (which Antonio violates not only be displacing his brother, but by selling out to the King of Naples, I.ii.133-7).

By what means does Prospero become qualified to resume his role as Duke of Milan?  In other words, describe how Prospero must reform in order to be qualified to resume rule.