Why was the italian coup unique in the history of the european theater in world war ii?

  Because they surrender against the Allies and break the relation with the Nazis.

Explanation:

  Shortly after the Allied powers invaded Italy under the code name Operation Husky on 1943. The Italian fascist regime fell rapidly into disrepute. They overthrown and arrested Benito Mussolini and put in his place a new provisional government that immediately started to secret arrange an armistice with the Allies.

  Because of this Germany had to deploy more armies in Italy to stop the Allies establishing air bases that could threaten Germany´s southern cities.

  I hope this answer helps you.

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