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A tux; dinner suit or simply a dark suit would be OK for the formal nights unless you will eat away from the main diningroom.
There are 2 dining rooms for anytime dining, both are very similar. if you eat in either of those on formal nights, you will need to wear a suit at the very least, but most people wear dinner suits. you can always go into the buffet which is not as hectic on an evening. you can wear what ever you like in there.