Got the quest today so thought I'd give it a try....
Gear is:
Head: Ending Hood
Glove: Ending Gloves
Chest: Ending Robes
Leg: Ending steps
Class: Ending Bond
Shader: the hcnged man
Emblem: Omen of chaos
Every time I complete a strike or win a cruicable match it doesn't count towards this bounty? Why?
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Only emblem, shader and the class item need to be equipped to make progress... no need to go full out DO. However, in saying that, there is a [url=https://www.bungie.net/en/Forum/Post/213318340/0/0]known issue with Y3 ROI class items not progressing faction quests for the exotic class item since the 2.4.0 update[/url] and bungie is investigating. In the meantime, you need to either equip a Y2 class item for your faction if you have one, or obtain the Y3 Spektar class item for progress to count. Spektar class items can be obtained from Chroma Armor packages upon your next rank up with your faction.