Flow coefficients ν_n for n = 2, 3, 4, characterizing the anisotropic collective flow in Au + Au collisions at  √S_NN 200 GeV, are measured relative to event planes Ψ_n, determined at large rapidity. We report ν_n as a function of transverse momentum and collision centrality, and study the correlations among the event planes of different order ν. The ν_n are well described by hydrodynamic models which employ a Glauber Monte Carlo initial state geometry with fluctuations, providing additional constraining power on the interplay between initial conditions and the effects of viscosity as the system evolves. This new constraint can serve to improve the precision of the extracted shear viscosity to entropy density ratio η/s.