  We consider schemes of neutrino mixing arising within the discrete symmetry
approach to the well-known flavour problem. We concentrate on $3\nu$ mixing
schemes in which the cosine of the Dirac CP violation phase
$\delta_\mathrm{CP}$ satisfies a sum rule by which it is expressed in terms of
three neutrino mixing angles $\theta_{12}$, $\theta_{23}$, and $\theta_{13}$,
and a fixed real angle $\theta^\nu_{12}$, whose value depends on the employed
discrete symmetry and its breaking. We consider five underlying symmetry forms
of the neutrino mixing matrix: bimaximal (BM), tri-bimaximal (TBM), golden
ratio A (GRA) and B (GRB), and hexagonal (HG). For each symmetry form, the sum
rule yields specific prediction for $\cos\delta_\mathrm{CP}$ for fixed
$\theta_{12}$, $\theta_{23}$, and $\theta_{13}$. In the context of the proposed
DUNE and T2HK facilities, we study (i) the compatibility of these predictions
with present neutrino oscillation data, and (ii) the potential of these
experiments to discriminate between various symmetry forms.
