You need to do some Vanguard Tiger strikes and get the 6 Vanguard marks per completed mission. You can get up to 100 vanguard marks per week. You will get a bunch of blue engrams from the strike which will increase your chance of getting a legendary drop. You really need to at least get some legendary armor and weapons so you can do the Weekly Heroic and eventually the Nightfall. That is where the real loot is before the raid. (which I have yet to do yet, the raid that is).
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Sadly I've completed the weekly heroic before, and still no legendaries. :(
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I would focus my next playing time grinding the Vanguard Tiger strikes and get as much Vanguard Marks as possible. I see you play crucible the most correct? What is your Crucible rank? Can you buy any from the Crucible Vanguard?