Two Different Schedules of Carboplatin, Paclitaxel, Gemcitabine, and Surgery in Treating Patients With Newly Diagnosed Stage IIIC or Stage IV Primary Epithelial Ovarian Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cancer

RATIONALE: Drugs used in chemotherapy, such as carboplatin, gemcitabine, and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells or by stopping them from dividing. Giving chemotherapy before surgery may make the tumor smaller and reduce the amount of normal tissue that needs to be removed. Giving chemotherapy after surgery may kill any tumor cells that remain after surgery. It is not yet known which treatment regimen may kill more tumor cells. PURPOSE: This randomized phase II trial is studying how well giving one of two chemotherapy regimens containing carboplatin, gemcitabine, and paclitaxel works in treating patients undergoing surgery for newly diagnosed primary stage IIIC or stage IV ovarian cancer, fallopian tube cancer, or primary peritoneal cancer.