One way to go about this would be to calculate the circular dispersion as in this answer. If you set the constant $c$ fairly high, ie. 2 or 3, you may view all observations outside the interval

$ \left[\hat\mu - c \hat\delta, \hat\mu + c \hat\delta \right]$

as outliers. In that answer, you may also find some code to visualize this.

One way to go about this would be to calculate the circular dispersion as in this answer. If you set the constant $c$ fairly high, ie. 2 or 3, you may view all observations outside the interval

$ \left[\hat\mu - c \hat\delta, \hat\mu + c \hat\delta \right]$

as outliers. In that answer, you may also find some code to visualize this.