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A pair of pants Sigma(0,3) is a building block of orientedsurfaces. The purpose of this paper is to determine thediscrete conditions for the holonomy group piof hyperbolic structure of a pair of pants.For this goal, we classify the relationsbetween the locations of principal lines and entries of hyperbolicmatrices in PSL(2,R).In the level of the matrix group SL(2,R), we will showthat the signs of traces of hyperbolic elementsplay a very important role to determinethe discreteness of holonomy group of a pair of pants.