It is known that neutrino oscillations may map \phi _ { e } : \phi _ { \mu } : \phi _ { \tau } = 1 : 2 : 0 , the initial flavor ratios of ultrahigh-energy neutrino fluxes produced from a distant astrophysical source , into \phi ^ { D } _ { e } : \phi ^ { D } _ { \mu } : \phi ^ { D } _ { \tau } = 1 : 1 : 1 at the detector of a neutrino telescope .
We remark that this naive expectation is only valid in the \mu - \tau symmetry limit , in which two neutrino mixing angles satisfy \theta _ { 13 } = 0 and \theta _ { 23 } = \pi / 4 .
Allowing for the slight breaking of \mu - \tau symmetry , we find \phi ^ { D } _ { e } : \phi ^ { D } _ { \mu } : \phi ^ { D } _ { \tau } = ( 1 - 2 \Delta ) : ( 1 + \Delta ) % : ( 1 + \Delta ) with \Delta characterizing the combined effect of \theta _ { 13 } \neq 0 and \theta _ { 23 } \neq \pi / 4 .
Current neutrino oscillation data indicate -0.1 \lesssim \Delta \lesssim + 0.1 .
We also look at the possibility to probe \Delta by detecting the \overline { \nu } _ { e } flux of E _ { \overline { \nu } _ { e } } \approx 6.3 ~ { } { PeV } via the Glashow resonance channel \overline { \nu } _ { e } e \rightarrow W ^ { - } \rightarrow~ { } { anything } .