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Join the new monarchy [spoiler]#hailthemonarch[/spoiler]
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Buy it from the Vangaurd. It's the only 100% guaranteed way to get Legendary gear and you might end up getting a couple pieces at random while your building your marks up.
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If you have the dlc you can get blue gear that has light on it from the roc strikes and once you get 75 marks (and vangaurd rank 2) you can buy a vangaurd piece of armor from in the tower. Also buy whatever exotic piece xur has for your class. After that you should be around 29 and you can do vog on hard or keeping farming marks for more vangaurd gear. I made a titan on friday and got to lvl 27 by sunday night this way
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do patrols , rank up vanguard to lvl 3 and BUY a weapon.
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doing the raids is the fastest way to get legendary items. if you aren't going to be doing much raiding, you are cutting yourself off from the one thing that will meet your need for quick items. the nightfall is basically your only other chance for quick items. everything else is more of a grind: vanguard, crucible or faction gear etc. These require purchasing by means of reputation and marks that take time and commitment. Strikes will yield gear as well, but sometimes i go days at a time without seeing anything in a strike. Sometimes i get several items a day this way, but not consistently. Like I said before, basically the raids and the nightfall are the sure-fire way to attain legendary or better loot in a hurry