  The \tau^-\to K^-\eta\nu_\tau decays have been studied using Chiral
Perturbation Theory extended by including resonances as active fields. We have
found that the treatment of final state interactions is crucial to provide a
good description of the data. The Breit-Wigner approximation does not resum
them and neglects the real part of the corresponding chiral loop functions,
which violates analyticity and leads to a failure in the confrontation with the
data. On the contrary, its resummation by means of an Omn\`es-like
exponentiation of through a dispersive representation provides a successful
explanation of the measurements. These results illustrate the fact that
Breit-Wigner parametrizations of hadronic data, although simple and easy to
handle, lack a link with the underlying strong interaction theory and should be
avoided.
  As a result of our analysis we determine the properties of the K*(1410)
resonance with a precision competitive to its traditional extraction using
\tau^-\to (K\pi)^-\nu_\tau decays, albeit the much limited statistics
accumulated for the \tau^-\to K^-\eta\nu_\tau channel. We also predict the soon
discovery of the \tau^-\to K^-\eta'\nu_\tau decays.
