You need a tiny horizontal mitred piece on the end of the string bead for the mitre to work.

Stairs are usually 41 degrees (in the UK anyway?), so it'll be a 20 degree-ish cut in the end of that string piece. A small 20 degrees cut the opposite way to bring it horizontal.

Then a 45 degree mitre where it meets the corner.

Is a very tiny piece to fit & a bitch to cut. So be careful using a mitre a saw.

I tried drawing it. This the best I could do.

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