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Showing that ArcSinh[2]/ArcCsch[2] is 3?

I hope I've just overlooked something very simple.
I want to transform ArcSinh[2]/ArcCsch[2] to 3, using just "knowledge"
already implemented in Mathematica. I tried FullSimplify first, and it
doesn't help. I tried several other things. For example,

TrigToExp[ArcSinh[2]/ArcCsch[2]]  yields

Log[2 + Sqrt[5]]/Log[1/2 + Sqrt[5]/2].

But then how should we transform that to 3?


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