  A measurement of correlations between event-plane angles $\Phi_n$ is
presented as a function of centrality for Pb-Pb collisions at
$\sqrt{s_{_{\mathrm{NN}}}}=2.76$ TeV. These correlations are estimated from
observed event-plane angles $\Psi_n$ obtained from charged particle or
transverse energy flow measured over a large pseudorapidity range $|\eta|<4.8$,
followed by a resolution correction that accounts for the dispersion of
$\Psi_n$ relative to $\Phi_n$. Various correlators involving two or three event
planes with acceptable resolution are measured. Significant positive
correlations are observed for $4(\Phi_2-\Phi_4)$, $6(\Phi_2-\Phi_6)$,
$6(\Phi_3-\Phi_6)$, $2\Phi_2+3\Phi_3-5\Phi_5$, $2\Phi_2+4\Phi_4-6\Phi_6$ and
$-10\Phi_2+4\Phi_4+6\Phi_6$. However, the measured correlations for
$2\Phi_2-6\Phi_3+4\Phi_4$ are negative. These results may shed light on the
patterns of the fluctuation of the created matter in the initial state as well
as the subsequent hydrodynamic evolution.
