Web2000, welcome to Reef Sanctuary. I'm going to blast you with a water hose of information so buckle up and understand I'm trying to help and not attacking you.
The cleaner shrimp will definitely help long-term. The immediate problem is there is some level of stress due to over crowding, poor water quality, or lack of nutrition that is causing stress in your tangs, thus weakening their immuno system and making them susceptible to ich.
You did not indicate how big your tank is, but in general, tangs require 48" of lateral swim room as a minmum. Michael Paletta recommends at least 180 gallons for three tangs.
The Cleaner Wrasses have dietetic requirements very similar to Mandarin fish and need a larger and more mature tank that will supply the amphipod and copepods needed for it to survive. Cleaner Wrasses have traditionally very low survival rates in home aquaria because of this.
Can you please provide a description of your tank including how it is set-up and the number and types of fish, corals, and invertebrates you have. How long has the tank been established and what are your water parameters? Please indicate what your tests show your levels of ammonia, nitrites, nitrates, and Ph, as well as specific gravity and temperature.
Again welcome to RS and we'll look forward to diagnosing what could be causing this. Hope you didn't lose your Cleaner Wrasse to the anenome!
:smirk: