You might have been just unlucky but the tank is new and tangs get ich easily. If it were me and I had lost a few, I'd go slow adding new fish. Tangs (any fish really) really should be quarantined before adding to your system. Once ich gets into your display - its really tough to get it out - if you really ever do.
Sounds like you've set up a nice system. If you can set up a quarantine tank - do it. If your just dying to add some new fish, I'd get 4 or five more chromis - they're peaceful, tough, do better and look cooler in schools. Plus the added bio-load will help mature your system. Wait a bit before adding anymore tangs.
When I first started up my system and didn't have a quarantine tank, my local LFS would let me pay for my fish and they would treat them and keep them for a two weeks in their quarantine - then I could pick them up and add them to my display fairly confident that they were bringing nothing with them.
Maybe they won't do it - maybe they will. If they're competent and confident in their stock they should. If its petco - well just get the quarantine tank.
Good luck.
