Normally spots as you describe are stress related and tangs and angels are more susceptible to developing such spots if they are not completely content. Be sure your water parameters are good. Tangs and angels have low tolerance for high nitrates. Offer a variety of high quality fish foods for omnivores. You may want to add a sheet of marine algae to the diet and clip it to your rocks or with a saltwater compatible lettuce clip. This is an excellent of source vegetable food for tangs and has the added benefit of the tang being able to nip and tear at it in the tank which is a behavior simulating what they do in nature. Also start using either zoecon or selcon supplement. Excellent for tangs, or any fish, but especially for tangs.