Climb on top of the shorter of the two square pillars in front. Jump to grab the stone slab handhold on the taller column. Jump up to grab the handhold above.
Climb around to the left and jump to grab the nearest handhold on the side of the building. Jump straight up to stand on this narrow ledge, which is just above and to the right of the closed gate and again to grab the handhold above.
Jump up once more and then climb a bit father until Lara is hanging from the uppermost handhold in this group.
Traverse to the left. Lara will clear the gap in the ledge without jumping. At the end of this ledge, lightly tap Jump + Left to reach the next handhold, which is one of three small stone slabs above a window-like opening.
Climb down and to the left and then drop to grab the windowsill. Pull up into the room.
Attach your grapple to the metal ring and step backward out the window. Lara's weight pulls the lever, raising the gate to the right.
When it's open all the way, adjust the length of the cable so Lara's feet are a little higher than the doorsill in front of the gate. Swing back and forth a couple of times. Then, when Lara swings to the right, jump into the doorway and go through before the gate closes again.
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