It is defiantly a good idea, and it can only help the tank. The shrimp may fight, but as tropheusmaster said, they may find their own spot and not. In a 75 gallon, I'm unsure if they would be likely to fight, I've never had a coral banded shrimp. Also, tangs require a large span of swimming space to be happy and healthy. You could keep a small tang in a 75 but when it really starts to grow large it will be very cramped in that tank. So approach the tang with caution if you decide to get one, and know that a large tang probably not be too happy in a 4' tank (I believe they are 4' long). Just my opinion, someone with more knowledge about tangs then me is sure to chime in.

Good Luck.