This Destiny 2 Artifacts Edge, The Tangle Lost Sectors page will explain where to find all the mini-dungeons within that area of the Nessus Patrol space.
If you want more information on how to find Lost Sectors and the rewards they offer, our Lost Sectors locations page can help.
Destiny 2 Artifacts Edge, The Tangle Lost Sectors
The three Lost Sectors in Artifacts Edge and The Tangle are:
The Orrery location
Location: From the bottom of the lift, head towards the big circular opening in the cliff to your left. On the right-hand side of the opening you'll find the symbol on a rock wall. From the symbol, turn right and head through the opening in the wall. Turn left and you'll enter a large, open room.
Strategy: In the large open room, there are no enemies in here, so cross to the blue-lit opening across the room. Now turn turn left, then right (there will be a gun symbol on the wall).
You'll immediately encounter some Vex. Take out the Goblins in front of you, then focus on the Hobgoblins on the far ledge. When they're dealt with, turn right and start sniping the Hobgoblins at the top of the far stairs.
Try and get precise headshots to reduce their chance of regeneration. There are lots of Goblins here, but no Furies so you shouldn't get too overwhelmed.
The boss, Thydron, looks tough but is actually press easy if you have a decent energy weapon (such as a high-level pulse rifle) to hand.
Drain his shield and pepper his health, but beware that there may still be a few Goblins and Hobgoblins waiting to ambush you. When he's toast, the loot chest can be found at the far end of the platform.
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Ancient's Haunt location
Location: Head to The Tangle in the north-west, and follow the outer cliff until you come across the symbol in a cave. If you are next to several large, round stone objects, are you a little too far north - so head left (west) from there until you drop down and find the cave.
Strategy: Once you pass through the cave entrance, turn left and you'll seen see an opening with some red moss around it. Pass through it, drop down then drop down again. Turn right, then right, the finally left to enter the main area.
This chamber is huge and you'll fight across the whole thing as you pursue the boss, Pakrion. The area is full of Goblins, with a few Minotaurs and Hobgoblins thrown in for good measure.
The floating Vex boss will be just around the corner at the far end, to the left. Take out the Hobgoblins around him, and strafe away from his exploding, purple attacks. Try and time your hits as his shield shows an opening.
Pakrion will keep retreating until he reaches a dead end, this is a great place to hit a super or a couple of grenades. The loot chest can be found just behind him. An opening to lead you back to the start of the large chamber you're in will be to the left of it.