I don't think you have to I just found this.
Hey there,
Xbox 360 players who wish to purchase Destiny: The Taken King ($40 USD) or the Collector's Edition Upgrade ($60 USD) can do so via the in-game prompt on the Director. The upgrades will not be available on the Xbox Marketplace, only the Legendary Edition and the full Collector's Edition
English
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I looked earlier it only showed collectors and legendary. I don't have tdb so that might be a problem