Sounds like ich for sure. First off your tank is way to small for any Tangs, much less three. I assume you did not QT. Someone probably came in with ich just not visible. The stress of so many tangs in such a small environment lowered the resistance and your fish all died because of it. This would not effect your inverts. Please do research before buying fish. I'm no tang police member but this was an uneducated move that cost the lives of all your fish.
Maybe the worst part, to get rid of ich your tank must be fallow for 72 days, or hyposalinity which will kill just about anything left in your tank.