I have a Black Shoulder Tang that's about 3.5" and wanted to add a Chevron Tang 4.5". Are they too similar in body shape that they may not get along with each other?
Consider adding the second tang in an acclimation box. Letting the old tang see the new one can help and many use this method with similar species to reduce aggression. Leaving the tang in the box for several days and up to a week has worked for me in the past. You can purchase one or make a box from a plastic bottle like the one gallon (GFO/carbon/calcium chloride) containers that BRS sells and then using a magnetic algae scraper to position your box near the surface of the aquarium. One magnet is in the box and one outside the glass. I drill holes in the container to allow water flow. I have also seen egg crate used to form a box connected with zip ties if you want a really large acclimation chamber.
In my yrs of fish keeping I found with tangs you will be better off adding 2 more at the same time that will give you 3 and in threes it keeps one from being picked on.
An introduction box can help assess if there is severe agression or not and of course to get the fish used to each other. it's not a total guaranty but is always a good idea. Good luck with them, they're both beautiful fish.