  We review the theory of orthogonal separation of variables on
pseudo-Riemannian manifolds of constant non-zero curvature via concircular
tensors and warped products. We then apply this theory simultaneously to both
the three-dimensional Hyperbolic and de Sitter spaces, obtaining an invariant
classification of the thirty-four orthogonal separable webs on each space,
modulo action of the respective isometry groups. The inequivalent coordinate
charts adapted to each web are also determined and listed. The results obtained
for Hyperbolic 3-space agree with those in the literature, while the results
for de Sitter 3-space appear to be new.
