= Solution
The difference of the two wave-vector labels is $(1,0,-1)$, an allowed <reciprocal lattice vector> because $1+0-1$ is even. <Bloch's theorem> of the lattice dynamical matrix therefore gives
$$
\boxed{\omega_\nu(1,0,0)=\omega_\nu(0,0,1)}
$$
for corresponding <phonon> branches. Neither individual odd-sum point needs to be a <reciprocal lattice> point. It is their \b[difference] that establishes equivalence. Structure factors and neutron <polarization> factors can still change the observed intensities at those two scattering vectors, so equal frequencies do not require identical measured spectra peak by peak in intensity.
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