A Petiha is always done before the actual singing of the Maftirim. As you can see on page 0.16, those three verses are chanted using the makam of the week as the base, it is totally improvised. Then, the hazanim go on to sing the maftirim of that week all in the same makam as the Petiha. The Petiha is sung in order to set the mode of the makam. The Mizmor that follows is chanted on the same makam after the pizmonim to close the singing, it is also in improvisation.