I have a copperband and he's the greediest of them all in my tank. He eats brine shrimp and picks on food on the live rocks 24/7.. eats non-stop!

Despite being discouraged by many LFS owners, I introduced a new tomato clown into my tank 2 weeks after the 1st tomato went in. Initially, the 1st tomato clown kept chasing and attacking the new one ... and the new one hid in one corner for 2 days. Then, I decided to take the 1st tomato out of the tank and bagged him up for 2 days.. Meantime, I shifted the live rocks around, made some new arrangements in the tank ... and I re-introduce him back into the tank again. My 1st clown thinks that he's in a new tank and now, both my clowns are getting along very well.

I don't know if this would work for your tang and copperband.. but it's worth a try.