How did Haiti successfully overthrow one of the world’s great empires?

They manage to untied the majority of the slaves into their revolutionary army.

Explanation:

Haitian revolution is considered as the most successful slave revolts in history. That region was specifically created by French empire to allocated slaves that're use to produce sugar cane.

Historically, slave revolts often did not get a lot of support from fellow slaves due to the overwhelming fear that they felt if the effort was unsuccessful.

But Haitian revolution was different. They were led by several charismatic revolutionaries ( such as Toussaint L'Ouverture)  who managed to convince the slaves to unite on the effort and throw the European out of their territories.

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