This page explains how to find the Rota Ooh shrine and solve the "Passing of the Gates" puzzle.
How to Reach the Shrine
This shrine can be seen from Central Tower if you look south. You can reach it by warping to the Oman Au Shrine and floating down from the Great Plateau onto the dirt path that goes next to the northern wall of the Great Plateau. Go west from there and continue to follow the dirt path. When it splits, go to the right, where you can see a stable in the distance. Climb the hill behind the stable to find the Rota Ooh shrine.
How to Solve the Shrine
There is a basket near a crystal switch. Use Cryonis in the water to climb into that basket, then shoot the crystal switch with an arrow. The area will rotate and you will be on the top.
From here, you can walk over the gates in the floor, then drop down to a treasure chest in the corner of the area. It contains a small key.
Then you can go out through the hole in the wall of this small room and go to the orange orb that is in the middle. Put it near the elevator where you entered the shrine.
There is an opening in the wall near where the orb was. Go through, then turn around and look for the crystal switch on the left. Shoot it to rotate the wall again. Then you can use the small key to open the door. (If you are on the wrong side of the door, fall into the water and swim to the other side). Open the locked door.
Now throw the orange orb into the basket that you rode in earlier, then hit the crystal switch to make the orange ball fall into the target hole. This makes a stone go up and down. Stand on that stone and look toward the far wall (opposite the elevator) then glide to the treasure chest at the top. It contains a Feathered Edge.
Then get back on the stone and when it launches you up, shoot an arrow at the crystal switch. Then the wall will rotate under you and there will be stairs to Rota Ooh, but watch your step because there is a hole after the stairs. Then go talk to Rota Ooh to get the Spirit Orb.