Erlotinib, Docetaxel, and Carboplatin in Treating Patients With Newly Diagnosed Stage III or Stage IV Ovarian Epithelial, Primary Peritoneal Cavity, or Fallopian Tube Cancer

DISEASE CHARACTERISTICS: Histologically confirmed ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer Stage III or IV disease The following histologic epithelial cell types are allowed: Serous adenocarcinoma Mucinous adenocarcinoma Clear cell adenocarcinoma Endometrioid adenocarcinoma Mixed epithelial carcinoma Undifferentiated carcinoma Transitional cell carcinoma Malignant Brenner tumor Adenocarcinoma not otherwise specified Must have undergone appropriate surgery for ovarian epithelial, primary peritoneal cavity, or fallopian tube cancer within the past 6 weeks No borderline ovarian tumor of low malignant potential PATIENT CHARACTERISTICS: Age 18 and over Performance status GOG 0-2 Life expectancy Not specified Hematopoietic Absolute neutrophil count ≥ 1,500/mm^3 Hemoglobin ≥ 8.0 g/dL Platelet count ≥ 100,000/mm^3 Hepatic Bilirubin normal Meets 1 of the following criteria: Alkaline phosphatase (AP) normal AND AST or ALT ≤ 5 times upper limit of normal (ULN) AP ≤ 2.5 times ULN AND AST or ALT ≤ 1.5 times ULN AP ≤ 5 times ULN AND AST or ALT normal No hepatic disease that would preclude study participation Renal Creatinine ≤ 2.0 mg/dL Creatinine clearance > 50 mL/min No renal disease that would preclude study participation Cardiovascular LVEF ≥ lower limit of normal* No poorly controlled arrhythmia No unstable coronary artery disease No myocardial infarction within the past year NOTE: *LVEF evaluation performed only on patients requiring it Other Not pregnant or nursing Negative pregnancy test Fertile patients must use effective contraception during and for ≥ 3 months after completion of study treatment No peripheral neuropathy ≥ grade 2 No other nonmalignant systemic disease that would preclude study participation No history of severe hypersensitivity reaction to docetaxel or other drugs formulated with polysorbate 80 No medical, social, or psychosocial factor that would preclude study participation No psychiatric or addictive disorder that would preclude giving informed consent No other malignancy within the past 5 years except nonmelanoma skin cancer or carcinoma in situ of the cervix or breast PRIOR CONCURRENT THERAPY: Biologic therapy No prior immunotherapy for this malignancy Chemotherapy No prior chemotherapy for this malignancy Endocrine therapy No prior hormonal therapy for this malignancy Radiotherapy No prior radiotherapy for this malignancy Surgery See Disease Characteristics No planned interval cytoreductive surgery Second-look surgery allowed Other More than 1 year since prior experimental or investigational therapy No concurrent therapeutic anticoagulation with warfarin