EU three, also known as EU big three, EU triumvirate, EU trio or simply E3, refers to France, Germany and Italy, a group that consists of the three large founding members of the European Union.  
It had also been used to refer to the grouping of France, Germany, and the
United Kingdom, especially during the negotiations with Iran from 2003.  
Germany, France and Italy were part of the original
Inner Six founders of the EU along with Benelux nations. The UK joined the European communities in 1973 and decided to leave in 2016.
Negotiations with Iran
The foreign ministers from the EU three in 2006
In 2003, France, Germany and the UK launched negotiations attempting to limit the
Iranian nuclear program, which led to the Tehran Declaration of 21 October 2003 and the voluntary Paris Agreement of 15 November 2004.  
 EU 3 + 3, more commonly referred to as the E3+3, refers to a grouping which includes the EU-3 and  China, Russia, and the United States. It was coined when these states joined the EU diplomatic efforts with Iran in 2006. In the United States and Russia, it is more commonly known as P5+1, which refers to the five permanent members of the UN Security Council plus Germany.
Italy took part in a number of these meetings between 2006 and 2007.
 In 2014, under the request of the Italian PM  Matteo Renzi, Foreign Minister Federica Mogherini was named High Representative of the EU as the negotiations approached a conclusion and came to an end with the elaboration of the Joint Comprehensive Plan of Action in 2015.
Determined to keep the European project intact in the wake of the UK's vote to
leave the European Union in 2016, France, Germany and Italy called for greater integration in various trilateral summits in Berlin, Paris and Ventotene.  
More recently France, Germany and Italy have agreed a common position about the  Paris climate agreement they have led a draft EU law to restrain Chinese acquisitions of European firms and technologies  and they lead the EU sanctions on  North Korea.
EU Big Three
Votes in the Council (pre-Brexit)
Uniting for Consensus
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