Accuratemock catalogues are essential for assessing systematics in the cosmological analysis of large galaxy surveys. Anisotropic two-point clustering measurements from the same simulation show some scatter for different lines of sight (LOS), but are on average equal, due to cosmic variance. This results in scatter in the measured cosmological parameters. We use the OuterRim N-body simulation halo catalogue to investigate this, considering the three simulation axes as LOS. The quadrupole of the two-point statistics is particularly sensitive to changes in the LOS, with subper cent level differences in the velocity distributions resulting in similar to 1.5 sigma shifts on large scales. Averaging over multiple LOS can reduce the impact of cosmic variance. We derive an expression for the Gaussian cross-correlation between the power spectrum multipole measurements, for any two LOS, including shot noise, and the corresponding reduction in variance in the average measurement. Quadrupole measurements are anticorrelated, and for three orthogonal LOS, the variance on the average measurement is reduced by more than 1/3. We perform a Fisher analysis to predict the corresponding gain in precision on the cosmological parameter measurements, which we compare against a set of 300 extended Baryon Oscillation Spectroscopic Survey emission-line galaxy EZmocks. The gain in f sigma(8), which measures the growth of structure, is also better than 1/3. Averaging over multiple LOS in future mock challenges will allow the redshift space distortion models to be constrained with the same systematic error, with less than three times the CPU time.