Circular symmetry criterion for a complex gaussian process

Question

Question: Circular symmetry criterion for a complex Gaussian process. Show that the distribution of the complex Gaussian process Z(t)e^iθ is invariant for all rotations 0 ≤ θ ≤ 2π if and only if the pseudo-covariance function Q_ZZ (t,s) = E[Z(t)Z(s)] = 0.