What do you mean by "stable"? Given that ## \theta ## increases (or decreases) at each time interval of length ## \omega ##, this is not a motion around an equilibrium position, so the usual concept of stability of an equilibrium position does not apply.
Another possible motion
https://dl.dropboxusercontent.com/u/503888/file2.gif
and the corresponding time diagrams
https://dl.dropboxusercontent.com/u/503888/graphics.png
This is a representation of one of the solutions, found with the NDSolve function of Mathematica, and by trial and error on the initial conditions:
https://dl.dropboxusercontent.com/u/503888/file.gif