  With the new viscous hydrodynamic + hadron cascade hybrid code VISHNU, a
rather precise (O(25%)) extraction of the QGP shear viscosity (eta/s)_QGP from
heavy-ion elliptic flow data is possible if the initial eccentricity of the
collision fireball is known with <5% accuracy. At this point, eccentricities
from initial state models differ by up to 20%, leading to an O(100%)
uncertainty for (eta/s)_QGP. It is shown that a simultaneous comparison of
elliptic and triangular flow, v_2 and v_3, puts strong constraints on initial
state models and can largely eliminate the present uncertainty in (eta/s)_QGP.
The variation of the differential elliptic flow v_2(p_T) for identified hadrons
between RHIC and LHC energies provides additional tests of the evolution model.
