Possible issues with random elements of `CircleGroup`?

[olivierverdier]

Consider the circle group

G = CircleGroup()

This works:

g = rand(G)

This also works, although it gives a tangent vector which is not stored as left invariant (this is fine, but worth being aware of it):

rand(G; vector_at=g)

---

Now:

This throws a MethodError:

rand(TangentSpace(G,g)) # same error if g == identity_element(G)

This only ever returns 0:

rand(G; vector_at=identity_element(G)) # 0.0

[olivierverdier]

Closing, since this is probably working as expected (see https://github.com/JuliaManifolds/Manifolds.jl/issues/688#issuecomment-1816051476).