  The neutrino mixing sum rule $\theta_{12} - \theta_{13}\cos(\delta) \approx
\theta^\nu_{12}$ provides a possibility to explore the structure of the
neutrino mass matrix in the presence of charged lepton corrections, since it
relates the 1-2 mixing angle from the neutrino mass matrix, $\theta_{12}^\nu$,
to observable parameters of the PMNS mixing matrix. The neutrino mixing sum
rule holds if the charged lepton mixing angles are CKM-like, i.e., small and
dominated by a 1-2 mixing, and for small 1-3 mixing in the neutrino mass
matrix. These conditions hold in a wide class of well motivated flavour models.
We apply this sum rule to present oscillation data, and we investigate the
prospects of future neutrino facilities for exploring the sum rule by
simulating various setups for long-baseline reactor and accelerator
experiments. As explicit examples, we use the sum rule to test the hypotheses
of tri-bimaximal and bimaximal neutrino mixing, where $\theta^\nu_{12}$ is
predicted by $\sin^2(\theta^\nu_{12}) = 1/3$ or 1/2, respectively, although the
neutrino mixing sum rule can be used to test any prediction for
$\theta^\nu_{12}$.
