  Calculation of moments of generalized parton distributions in lattice QCD
requires more powerful techniques than those previously used to calculate
moments of structure functions. Hence, we present a novel approach that
exploits the full information content from a given lattice configuration by
measuring an overdetermined set of lattice observables to provide maximal
statistical constraints on the generalized form factors at a given virtuality,
t. In an exploratory investigation using unquenched QCD configurations at
intermediate sea quark masses, we demonstrate that our new technique is
superior to conventional methods and leads to reliable numerical signals for
the n=2 flavor singlet generalized form factors up to 3 GeV^2. The contribution
from connected diagrams in the flavor singlet sector to the total quark angular
momentum is measured to an accuracy of the order of one percent.
