I see now that Andrei would like to know what to do when the distribution has 2 modes and is symmetric about these modes. It seems better to just give a second (more detailed) answer rather than complicate the simple answer I gave above (basically I think the idea in gowers comment above is sound, but it's a bit tricky to actually implement).
So, how do we deal with estimating the 'mean direction' of a distribution that looks something like:
Good questions at this point are ''what is mean direction anyway?'' and specifically for the distribution above ''does a mean direction even exist?''
This has been a question I have been looking at a few months now. I'm wary of blowing my own horn a bit here, but I am going to attach a part of my thesis which I think gives satisfactory answers to these questions (I would love to give you the whole thesis, but it's not quite ready for the public to see). I suggest that there are (at least) two different, but equally reasonable and intuitive definitions of mean direction. I argue that the distribution above has no mean in a rigorously definable sense for both of these definitions.
Given $N$ data points $\Theta_1,\dots, \Theta_N$ on a circle there exist very accurate and efficient O(N)-time algorithms to estimate both of these means if they exist. Neither algorithm will converge if used on circular data drawn from the bimodal distribution above as (according to my definition) the means do not exist.
Still, given $N$ data points $\Theta_1,\dots, \Theta_N$ drawn from the bimodal distribution above, if what you want to do estimate one of the ''modes'' rather than the mean direction, then my gut tells me that there probably are efficient and accurate algorithms to do this, although I don't know if they exist in the literature. You could try Fishers book The Statistical Analysis of Circular Data.
