Under which circumstances would you consider filing an amicus brief in an appeals case?

An amicus curiae brief in support of a petitioner or appellant shall be filed within 30 days after the case is placed on the docket or a response is called for by the Court, whichever is later, and that time will not be extended.

on june 23, 1972, the president signed title ix of the education amendments of 1972, 20 u.s.c. into law. title ix is a comprehensive federal law that prohibits discrimination on the basis of sex in any federally funded education program or activity.