you have ich in your display tank
If you catch the tang and treat him in QT or with dips, when he goes back in your tank he will become infected again. If you don't want ich in your tank, all of the fish need to come out and the tank needs to sit fishless (fallow) for 6-8 weeks while the fish go through hypo or copper to eliminate the parasites on them. This is the only way to rid your system of the parasite and make sure the tang doesn't die or that the ich spreads to other fish.
I would guess you have had ich in your tank for quite some time and something has happened which has stressed the tang thus lowering his immunity to the parasite and now he is showing clinical signs of disease. I keep several tangs and only my powder blue occasionally shows a few ich spots. I run a lot of UV on my system and I believe that it helps keep the parasite burden reduced in my tank. I have ich in my tank but its not much of an issue to my fish.
The best thing to do is to rid your system of ich, but a lot of time it is not practical to QT and treat all of the fish. You can try beefing up the diet, UV, cleaner shrimp/fish, or any of those other things people have anecdotally "cured" their ich with but there is only one definitive solution. Best of luck!