(1) All teachers employed full time in the public schools shall be members of the system except alien teachers who have been granted a temporary permit to teach as exchange teachers.
(2) A minimum of ninety days or the equivalent of ninety days of employment during a fiscal year shall be required to establish membership. A teacher shall be considered as employed full time if serving regularly for four-fifths or more of a school day or if assigned to duties which are the equivalent of four-fifths or more of a full time assignment. A teacher who is employed for less than full time service may become a member by filing an application with the retirement system, submitting satisfactory proof of teaching service and making the necessary payment before June 30 of the school year immediately following the one during which the service was rendered.
(3) After June 30th of the school year immediately following the one during which the less than full-time service was rendered, the necessary payment may be made under RCW
41.50.165(2).