  We propose a simple but useful parametrization of the flavor composition of
ultrahigh-energy neutrino fluxes produced from distant astrophysical sources:
$\phi^{}_e : \phi^{}_\mu : \phi^{}_\tau = \sin^2 \xi \cos^2 \zeta : \cos^2 \xi
\cos^2 \zeta : \sin^2 \zeta$. We show that it is possible to determine or
constrain $\xi$ and $\zeta$ by observing two independent neutrino flux ratios
at the second-generation neutrino telescopes, provided three neutrino mixing
angles and the Dirac CP-violating phase have been well measured in neutrino
oscillations. Any deviation of $\zeta$ from zero will signify the existence of
cosmic $\nu^{}_\tau$ and $\bar{\nu}^{}_\tau$ neutrinos at the source, and an
accurate value of $\xi$ can be used to test both the conventional mechanism and
the postulated scenarios for cosmic neutrino production.
