Blue tangs with spots can be a bit tricky to diagnose. It does not have HLLE, but those spots could be one of two issues: marine ich, or mucus plugs. Ich is a very serious disease and would need to be treated. Mucus plugs are a skin reaction that blue tangs do when stressed. The trouble is, ich itself can cause them!
With ich, the spots come and go and change location every days or so, but with a generally increasing trend. Mucus plugs tend to produce slightly larger spots that stay in the same location longer.
How long have you had the fish?
How long has it had these spots?
What other animal are in with it?
So - what to do? I would treat for ich with copper in a quarantine tank, just to be safe, but that can be difficult to do if you are not set up for that.