Circular estimation problems arise in many applications and can be addressed with methods based on circular distributions, e.g., the wrapped normal distribution and the von Mises distribution. To develop nonlinear circular filters, a deterministic sample-based ap-proximation of these distributions with a so-called wrapped Dirac mixture distribution is beneficial. We present a closed-form solution to obtain a symmetric wrapped Dirac mixture with five components based on matching the first two trigonometric moments. Furthermore, we discuss the choice of a scaling parameter involved in this method and extend it by superimposing samples obtained from different scaling parameters. Finally, we propose an approximation based on a binary tree that approximates the shape of the true density rather than its trigonometric moments. All proposed approaches are thoroughly evaluated and compared in different scenarios.