  We consider a left invariant Riemannian metric on SO(3) with two equal
eigenvalues. We find the cut locus and the equation for the cut time. We find
the diameter of such metric and describe the set of all most distant points
from the identity. Also we prove that the cut locus and the cut time converge
to the cut locus and the cut time in the sub-Riemannian problem on SO(3) as one
of the metric eigenvalues tends to infinity.
