If your tang is eating and is acting normally then I'd just leave it be and let it fight the ich on its own, doing what you can to keep water parameters in good condition and minimizing stress. The two ways to treat for ich are hyposalinity or copper, both of which need to be done outside of the main tank. And there really isn't any point in putting the fish through the stress of being caught, quarantined, and treated unless you do so with all of your fish, leave the DT fallow for at 12 weeks, and then proactively treat every fish before you add it to your DT from here on out - otherwise you will always still have ich in your system that can rear its head at any time. As long as you keep the fish stress free and water parameters good, they will likely be able to fight it off on their own and you won't have a problem.
If your tang recovers and then the ich returns, you might want to consider rehoming as the tank size might be contributing to stress.... stress = lowered immunity = greater likelihood of disease. I only say this as something to think about in the future if he doesn't get and stay healthy, not trying to turn this into a tang discussion. Some tangs do just fine in a 4ft tank, and I think the purple tang can do fine in that size for a period of time, but as they get large then may need a larger home.
If the tang doesn't fight it on his own and stops eating or begins to hang at the bottom, hide in the rocks, breath heavy, then I'd strongly consider trying to catch him and move him into a treatment tank.
One other option - a guy I know on another forum removed all of his corals, rock, and inverts from his DT tank, and then did a hyposalinity treatment on his DT for 12 weeks, then moved the rocks, corals, and inverts back into the DT and plans to QT and treat future additions. If you absolutely have to go a treatment route and can't set up another tank, then you could move everything but the fish into a rubbermade tub for 12 weeks and treat with hyposalinity.
