Immediately after the filing of the petition as provided in section 46-575, the board of directors of such district shall (1) by order fix a place and time, not less than ninety days nor more than one hundred twenty days after the petition is filed, for hearing thereon, (2) cause notice by publication to be made of the pendency of the petition and of the time and place of hearing thereon, and (3) forthwith cause a copy of the notice to be mailed by certified or registered mail to the county boards of each of the several counties having territory within the tract or tracts of land proposed to be annexed.