Three Dog's Head Wrap

If one chooses to kill Three Dog it can be obtained off his corpse.

Another option is to place a headgear with a higher DR (e.g. Tesla Helmet.) I went into sneak mode (hidden) and placed the helmet into his inventory without getting caught. Left the room and came back, he had the helmet on, and Three Dog's Glasses and Three Dog's Head Wrap was in his inventory. I went back into sneak mode and tried stealing both items, got caught. Tried stealing the glasses by itself and was successful. Then tried stealing the helmet and got caught. I switched my Tesla Armor to Ranger Battle Armor and was successful in stealing his head wrap. No armor might have proven a success too. My sneak was 100 and did not use a stealth boy. Any glasses and Head Wrap can use to repair the two apparels respectively.