This type of question is not what this Questions forum is intended for. You should post this type of question in your Notebook or in a Discussion.

In addition to the comments above, in English there are very few countries which have the definite article ("The") in front of their name. It's common in Italian and may be in some other languages, but not in English. There are a few exceptions to this; for example "Sudan" is still sometimes referred to as "The Sudan" and Lebanon USED to be referred to as "The Lebanon" (though that usage is now largely extinct) but Britain has never been "The Britain" but rather Britain, or Great Britain, or the United Kingdom (depending on context).

The slang word in the English-language news media is "Brexit": Britain + exit = Brexit

"Do you support Britain leaving the EU?" is the correct way of asking the question. After Britain leaves it will be "out of the EU".