  The rigidity of marked length spectrum for closed hyperbolic surfaces due to
Fricke-Klein [7] has been the motivation of many different rigidity results,
specially for manifolds of negative curvature. From the works of Vigneras [18],
Sunada [17] and many other authors this result is far from being true for the
unmarked length spectrum. The purpose of this paper is to introduce a closely a
related unmarked spectrum, the length-angle spectrum, and show that it
determines the surface uniquely.
