Bond Orientational Correlation Function

Firs this question has some similarity with Bond order correlation function and Bond Orientational Correlation Function – how exactly to calculate but its a little bit different , so having those context i am going to evaluate the bond orientational correlation function which has the form $$g_6(x=|x_i – x_j|) =langlepsi_6(x_i) psi_6^*(x_j)rangle .$$ where $$psi_6(x_i) = frac{1}{N_i}sum_{i=1}^{N_i}{exp(i6theta_i^j)}$$
is the 6-fold local orientational order and $N_i$ is the number of nearest neighbors of particle $i$ and can be evaluated using voronoi weighted method.
and $theta_i^j$ is the angle between the line connecting the particle $i$ with $j$.

however I get confused by the meaning of this $langle *rangle$ what kind of average is this exactly? does anybody had ever evaluated it? since eventually i would like to calculate it in a computer , perhaps a python code or some hints might also be usefull.