It’s a field of broken dreams.

The city Department of Education spent $4 million in taxpayer funds to renovate a Brooklyn athletic field — then handed it to a small all-boys public school founded by former Chancellor David Banks, which promptly kicked out three girls’ soccer teams.

The power play by Eagle Academy for Young Men II in East Flatbush is under scrutiny by the feds for alleged violation of Title IX, which bars sex discrimination in public schools, The Post has learned.

Until last fall, the girls’ varsity soccer teams from Medgar Evers College Prep, Wingate and Prospect Heights high schools — all in District 17 and within walking distance of the “Old Boys and Girls Field” at the corner or Troy Avenue and Rutland Road — used the space for practice and home games. 5

But th

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