The angels & tangs won't eat this type of marine algae generally known as maiden's hair ( Chlorodesmis sp. ) and this type of macro algae is not easy to keep and won't last long for fish only system and it requires strong water flow & intensive light. If you introduce the caulerpa sp. next time as you mentioned, your fish will definately finish the caulerpa in seconds. HTH
Just in case when you discover your maiden's hair algae is turning lesser green or doesn't retain its natural color and starts to change white from bottom to top and that's a symptom the hair is starting to loose off from the substrate until nothing or no filament is left behind on the rock surface. No worries, just keep the rock without throwing it away for the algae will grow again once the condition is favourite to it and this will take a few weeks or even a few months. Have fun & this algae is classified as an advanced level to keep in captivity.