했지 and 했죠 are the same thing. The first is used in the 'blunt form' (So when talking to close friends or family) and the second is a contraction for the informal polite ending. 했지요-->했죠 Both of these mean our equivalent of 'Right?' Like, 'You're going to the store, right?' or 'You know I don't like red meat, right?' As for 했어 again it's a shortend grammar feature. Normally it'd be 했어(서) but Koreans love shortening words and grammar. Basically it's a 'because' or 'due to' grammar. Like, 'I woke up late, so I was late to class.' or 'Due to the rain I was late to work'. The 해 in this is from 하다 and is basically the Korean verb to 'do' something. '했어요!' 'I did it!' Then the 'ㅆ어서' for the most part means that 'because of' or 'due to' I mentioned a moment ago. If you're not too familiar with Korean it might be a little to take in so I'm sorry if I fire hosed you with this. If you have any questions shoot me a message and I'll try to explain it again.

or when someone feels sure one's opinion, they used to use it. 내말이 맞죠? = It's correct what I said, Isn't it?

했죠 is used for sarcasm :D