Cisplatin and Paclitaxel in Treating Patients With Stage IIB, Stage IIC, Stage III, or Stage IV Ovarian Epithelial Cancer, Fallopian Tube Cancer, or Primary Peritoneal Cavity Cancer

Inclusion Criteria: * Histologically confirmed ovarian epithelial, fallopian tube, or primary peritoneal cavity cancer * Stage IIB, IIC, III, or IV disease * Optimal or suboptimal residual disease after debulking surgery within the past 12 weeks * Appropriate tissue for histologic evaluation available * The following histologic epithelial cell types are eligible: * Serous adenocarcinoma * Endometrioid adenocarcinoma * Mucinous adenocarcinoma * Undifferentiated carcinoma * Clear cell adenocarcinoma * Mixed epithelial carcinoma * Transitional cell carcinoma * Malignant Brenner tumor * Adenocarcinoma not otherwise specified * Carcinosarcoma * No ovarian epithelial carcinoma of low malignant potential (borderline carcinomas) * No synchronous primary endometrial cancer or a history of primary endometrial cancer unless all of the following conditions are met: * Stage ≤ IB disease * No more than superficial myometrial invasion, without vascular or lymphatic invasion * No poorly differentiated subtypes, including papillary serous, clear cell, or other FIGO grade 3 lesion * GOG performance status 0-2 * ANC ≥ 1,500/mm\^3 * Platelet count ≥ 100,000/mm\^3 * Serum creatinine ≤ 1.5 times upper limit of normal (ULN) * Bilirubin ≤ 1.5 times ULN * Alkaline phosphatase ≤ 2.5 times ULN * SGOT ≤ 2.5 times ULN * Audiograms required after study chemotherapy courses 3 and 6 for patients with hearing loss, or who are experiencing tinnitus during study therapy * Negative pregnancy test * Not pregnant or nursing * Fertile patients must use effective contraception * None of the following: * Septicemia * Severe infection requiring parenteral antibiotics * Malnutrition requiring parenteral hyperalimentation * Acute hepatitis * Any other major medical conditions expected to interfere with completion of protocol therapy * No active bleeding * No circumstances that would prohibit completion of study therapy or required follow-up * No history of allergic reaction to polysorbate 80 (e.g., etoposide or vitamin E) * No other invasive malignancies, except for nonmelanoma skin cancer or other specific malignancies within the past 5 years, or whose previous cancer treatment contraindicates this protocol therapy * No unstable angina or myocardial infarction within the past 6 months * Abnormal cardiac conduction (e.g., bundle branch block or heart block) that has been stable for the past 6 months allowed * No prior targeted therapy for the management of ovarian epithelial or primary peritoneal cavity cancer including, but not limited to, the following: * Vaccines * Antibodies * Tyrosine kinase inhibitors * No prior chemotherapy * No prior radiotherapy * No prior hormonal therapy for the management of epithelial ovarian or primary peritoneal cavity cancer