This question has been answered. Nothing to see here, move on.
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Edited by Lostypoo: 4/14/2016 8:41:11 PMThe Spektar armor you have equipped (Spektar Kallipolis cloak), cannot be used towards the exotic fact in class item quest sorry. Bungie is aware of this issue and investigating. https://www.bungie.net/Mobi/en/About/Article?id=44590