The onset follows the way an infection of Marine Velvet (
Amyloodinium ocellatum) would progress. I hope it isn't that. In case you're not aware of this disease:
http://www.reefkeeping.com/issues/2004-07/sp/feature/index.php
Sometimes the onset of MV is so fast, all the aquarist knows is going on is that their fish is breathing fast. It's one of those "disease" end of the spectrum possibles I first mentioned in my first post. Tangs, as a matter of fact are usually one of the fish that succumb to this disease early on.
Watch your other fish
very closely. You're looking for rapid breathing, any signs of flashing (scratching on surfaces), shaking their head (wagging), darting suddenly, and showing tiny white spots (that are hard to see even when you know what you're looking for). The above article will help you with what to look for.
When was the last fish or specimen you added to the system and did you quarantine it before putting it in the display?
You might start thinking about how you would treat your fish if this is a disease.
If you're lucky, the fish died of something that wasn't 'catching' or likely to spread.
Look very closely at all your fish at least twice a day. If you still have the dead fish, look closely at it and see if you can see any spots on it, signs of infestation, flukes, worms, etc. I don't know your profession, so I don't know if you are able to perform any kind of post mortem investigation, but if you can't do this and you are
really motivated, take the dead fish to your nearest and largest public aquarium or college where they have people that can and are willing to perform such a post mortem.
Until something else develops that's about all I can say. Monitor the tank specimens closely. Do the large water changes for the next 2 or 3 days and see what reaction the fish have to the new water. Look for any difference (increased appetite, more active, more in the open (less hiding), etc., etc.) between the before and after water changes behavior or appearance.
I'm sorry for your loss. Considering the bio-load you have going, I would recommend not replacing this guy.