Plumbing Coupling Puzzle

First I made an attempt to solve this puzzle by pulling all the string to the center and unangling it there. This proved to be a fruitless pursuit. I only tangled it more.

I then worked it back to the way it originally was. At that point I decided it must be solved like the other topological puzzles. I thought on that and figured that if the knot could be brought outside it would be much simpler.

So I worked that out with the string and found a solution.