Go back around to the south side of the gilded tower. Climb onto the fallen pillar, turn around, jump onto the squat pillar, and from there jump to grab the ledge on the middle level of the tower.
Pull up and advance cautiously. As Lara passes over the crumbling floor it will give way.
If you don't immediately jump forward, she'll fall into the spike pit below.
Once you've made it past the trap, turn around and activate Survival Instinct to spot a document (3/4) sitting in the dark corner to the left of the spike pit. Examine the scroll, titled The Knight: On the Tail from the Prophet's Trail series, for XP and Greek proficiency.
Now continue out the other side of the tower. Jump to grab the freestanding column, pull up, and turn left.
The final incense burner (7/7) is hanging directly ahead. Shoot it down. If you have destroyed all of the others, you'll complete the Hang 'em High challenge and receive 150 XP plus 2,000 Expedition Credits if it is your first time completing this challenge. If you missed any, you can either backtrack for them or return to Syria later after beating the game.
Turn around so Lara's back is toward the gilded tower and swim along the right wall to the far alcove, where you'll find a container with a Byzantine Coin inside.
Jump over the cracked floor concealing another spike pit.
Then advance carefully. Either jump over the square button on the floor to avoid triggering the swinging spike trap ahead...
...or trigger it and then quickly shoot the 2 wooden blocks before the spikes reach you. You'll get a small XP award if you destroy the trap. Then continue to the end of the passageway.