If you are having a hair algae issue, then you have too many nutrients in the tank. Nutrient export is a multi-prong strategy. Here is what I do:
1. Carbon use, changing it out regularly
2. GFO use, changing it out regularly, regular water changes. In my case a 1% daily change with a double headed pump.
3. Regular use of filter socks for mechanical filtration, removed and rinsed/replaced every two days.
4. Protein skimming, keeping the skimmer neck clean. I use a neck cleaner, but otherwise cleaning the cup/neck once weekly.
5. Sulfur denitrator. I have and use one. They work very well. I would not say they are a requirement. Use of the other strategies I have listed would probably get you where you need to go regarding nitrate and phosphate levels
6. Judicious feeding. You'd be surprised how the root of many HA issues is r/t over feeding. Not saying this is your issue, but you could look at it and see if it applies.
7. I have Mexican Turbo Snails in my tank. Nothing better for eating HA, IME, hands down. Other snails have the name "Turbo" attached to them, but are not Mexican turbos.
8. Regular testing for PO4 and NO3 to alert you in case you ned to up your above techniques.
Now the regimen above is what I do to maintain a relatively algae free environment in my 465. What you can do now to get rid of your existing alges is:
1. Manually remove it using a tooth brush or other plastic stiff bristle brush, incorporating it as part of a water change.
2. Add your Mexican Turbo Snails now, as they start eating as soon as they hit the tank.
3. Buy a sea hare. They will mow down hair algae fast, but after you have it under control, you will need to remove and rehome the Hare, as it will stave and die without hair algae to eat.