You can't get quest exotics.
You can't get a exotics for a class different than the one you used to get the fated engram
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I know i cant get quest exotics, but nowhere is it stated within the engram that you cant get an exotic that is for another class, just that if there is one that isnt within your collection you will get it. Not saying your not correct, just saying its pretty misleading that it is the way that it is if thats the case :/