  In this work, we calculate radiative vertex $VP\gamma$ ($V=\phi,\omega,\rho$
and $P=\eta,\eta'$) by utilizing $\omega-\phi$ mixing scheme and taking into
account the contributions of the three-particle twist-4 distribution amplitudes
of the photon in QCD sum rules on light cone. According to experimental data of
$V\rightarrow P\gamma$ and $P\rightarrow V\gamma$ from PDG, a value of the
$\eta-\eta^\prime$ mixing angle, $\phi=(40.9\pm0.5)^\circ$, is extracted in the
framework of the quark-flavor basis to describe the $\eta-\eta^\prime$ system.
