  We present the first calculation of the cross-correlation between
three-dimensional cosmic shear and the integrated Sachs-Wolfe (iSW) effect.
Both signals are combined in a single formalism, which permits the computation
of the full covariance matrix. In order to avoid the uncertainties presented by
the non-linear evolution of the matter power spectrum and intrinsic alignments
of galaxies, our analysis is restricted to large scales, i.e. multipoles below
l=1000. We demonstrate in a Fisher analysis that this reduction compared to
other studies of three-dimensional weak lensing extending to smaller scales is
compensated by the information that is gained if the additional iSW signal and
in particular its cross-correlation with lensing data are considered. Given the
observational standards of upcoming weak lensing surveys like Euclid, marginal
errors on cosmological parameters decrease by ten per cent compared to a cosmic
shear experiment if both types of information are combined without a CMB prior.
Once the constraining power of CMB data is added, the improvement becomes
marginal.
