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To get past the third screen you need to get in the squared part and hit some buttons (red dots), then you climb out of the square (and I think that is the hardest part here) and find another button outside it. After pressing that button the a gate in the lower right will open and a raft wil float to the left. You have to drop on it and float to the next screen with the two rats. Tip when you swing with your web you can't get grip on the green colored stones (they R slippery).

I hope it solves a part of the sewer mystery.