  We consider the class of positive bounded and semi-continuous functions
defined on the two dimensional torus If f belongs to this class, then f will be
considered as the symbol of a Toeplitz operator truncated on a triangle
parametrised by an integer number . We develop a geometric structure of the
inverse of the Toeplitz operator and give an asymptotical development of the
trace of its inverse wich brings out the geometry of the triangle. The
foundation of this result consists in the possibility of f having a
factorisation of type |g|^2 where the spectrum of g will be localised in a
given semi-cone. This trace theorem allows in particular to find again the
Linnik-Szeg\"o theorem about the asymptotical evaluation of the determinant of
the truncated Toeplitz operator (or Toeplitz matrix)
