A good rule of thumb with tangs is that you never try to keep two of the same species or two tangs that have a similar shape together. I maintain a 240 gallon fish only tank that I have three yellow tangs that do just fine together. If you were to add two more tangs at the same time, like a purple and a sailfin or some other species, that might work. You'll have to understand that they might fight a little at first, and that it could end badly... In a 125 you might want to stay with one species of tang, like the yellow. Or, you could trade the yellow and get a purple (if you could catch him!). Generally angels don't like other fish that have the same shape they do, or similar colors. You could probably get away with keeping a Queen angel with a Majestic, but at over $100 each, you wouldn't want to risk having one of them die. I believe it is best to keep only one "large" angel in a tank, but you can usually mix pygmy angels, as long as they don't look too much alike. A flame and coral beauty could live together fine. There are always exceptions, as each fish has his own personality. Some flame angels are bad about nipping corals/clams, others don't touch them.
Sonny