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The authors find geodesics, shortest arcs, diameter, cut locus, and conjugatesets for left-invariant sub-Riemannian metric on the Lie group SO(3), undercondition that the metric is right-invariant relative to the Lie subgroup$SO(2)\subset SO(3)$.

(Locally) shortest arcs of special sub-Riemannian metric on the Lie group SO(3)