How good is μ-τ symmetry after results on non-zero θ13 ?

Viability of the interchange symmetry imposed as an approximate symmetry (1) on the neutrino mass matrix M-nu f in the flavour basis (2) simultaneously on the charged lepton mass matrix M iota and the neutrino mass matrix M-nu and (3) on the underlying Lagrangian is discussed in the light of recent observation of a non-zero reactor mixing angle theta(13). In case (1), mu-tau symmetry breaking may be regarded as small (less than 20-30%) only for the inverted or quasidegenerate neutrino mass spectrum and the normal hierarchy would violate it by a large amount. The case (2) is more restrictive and the requirement of relatively small breaking allows only the quasidegenerate spectrum. If neutrinos obtain their masses from the type-I seesaw mechanism then small breaking of the mu-tau symmetry in the underlying Lagrangian may result in a large breaking in M-nu f and even the hierarchical neutrino spectrum may also be consistent with mildly broken mu-tau symmetry of the Lagrangian. Neutrinoless double beta decay provides a good means of distinguishing above scenarios. In particular, non-observation of signal in future experiments such as GERDA would rule out scenarios (1) and (2).