I just finished all of Petra's and variks' quests, and I thought that's how you get Boolean Gemini but it didn't give it to me.
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Boolean Gemini requirements... 1. Taken War : Petra 2. Lost and Found 3. Wolves on Mars 4. Rank 3 with Queen 5. Patrol must be unlocked on Dreadnaught You may get and/or do these in any order and some may not even be available until you do other things. But once all are done Petra will call on you.