  Correlations of symmetry planes are important observables used to quantify
anisotropic flow phenomenon and constrain independently the properties of
strongly interacting nuclear matter produced in the collisions of heavy ions at
the highest energies. In this paper, we point out current problems of measuring
correlations between symmetry planes and elaborate on why the available
analysis techniques have a large systematic bias. To overcome this problem, we
introduce a new approach to approximate multi-harmonic flow fluctuations via a
two-dimensional Gaussian distribution. Employing this approximation, we
introduce a new estimator, dubbed Gaussian Estimator (GE), to extract pure
correlation between symmetry planes. We validate GE by using the realistic
event-generator iEBE-VISHNU and demonstrate that it outperforms all existing
estimators. Based on event-shape engineering, we propose an experimental
procedure to improve GE accuracy even further.
