Just to throw my hat in the ring...
The whole 'odd number of tangs so they don't fight' is hogwash. I heard the same nonsense when I was starting out from my LFS and so I tried it in my old 210 with 3 juvi yellow tangs. They were only juvie's and still didn't tolerate each other. It was nothing MAJOR, but I HATED the nipped fin look. Made them look ratty.
Another thing I hate reading here is that tangs of different genus will get along. Color and shape are not the only criteria to consider. The FIRST thing to look at is, how big is the tank? How big are the tangs in question? What is the temperment of each, and what was the order they were added??
Tangs don't like food competitors, ie: other tangs. No matter the genus. For example, just because a yellow tang and powder blue tang are different genus and different colors, doesn't mean they'll be chummy. Try that lineup in a 55 and you'll see what I mean. If you're wanting to keep those 2 fish, you'd get a bigger yellow than pbt and add the yellow first. If your tank is large enough and you're adding an achilles or sohal etc...make sure it's added last and on the smaller side. There are MANY MANY MANY things to consider when adding tangs to your tank. None of which should be mirrors and taped pictures on the outside of the tank. That always kills me. If a fish is qt'd and healthy...and added at the right size, to the right lineup, in the right sized tank, in the right order, you'll be less likely to have issues.
Less likely. Because you can do everything right and still have issues. Nothing is a gurantee. Fish are like people, they are all different.

You might get a naso that didn't get the memo that he's supposed to be docile.