  We solve, by means of a nested coordinate Bethe ansatz, the open-boundaries
scattering theory describing the excitations of a free open string propagating
in $AdS_5\times S^5$, carrying large angular momentum $J=J_{56}$, and ending on
a maximal giant graviton whose angular momentum is in the same plane. We thus
obtain the all-loop Bethe equations describing the spectrum, for $J$ finite but
large, of the energies of such strings, or equivalently, on the gauge side of
the AdS/CFT correspondence, the anomalous dimensions of certain operators built
using the epsilon tensor of SU(N). We also give the Bethe equations for strings
ending on a probe D7-brane, corresponding to meson-like operators in an
$\mathcal N=2$ gauge theory with fundamental matter.
