Chemotherapy Before Surgery and Radiation Therapy or Surgery and Radiation Therapy Alone in Treating Patients With Nasal and Paranasal Sinus Cancer That Can Be Removed by Surgery

Inclusion Criteria: * Eastern Cooperative Oncology Group (ECOG) performance status of 0 or 1 * General physical condition compatible with the proposed chemotherapy and surgery * Stage T3 or T4a, histologically-confirmed NPNSCC requiring orbital or skull base resection: * Stages T3 and T4a disease will be included regardless of nodal status (N0 or N1-3), provided that surgical therapy would require orbital or skull base resection * The surgical oncologist in each institution will determine the need for resection of the orbit OR base of skull at baseline for patients on both Arms A and B and following neo-adjuvant chemotherapy for patients on Arm B * Resection of skull base will be deemed necessary according to skull base bone erosion by CT or marrow involvement by MRI is noted; for any disease abutting the skull base; or for ethmoid sinus or frontal sinus involvement * Resection of orbital contents will be deemed necessary according to skull base society guidelines, based on involvement of periorbital fat documented by MRI imaging * Patients must be deemed surgically resectable by the surgical teams at each institution and must have a determination of degree of anticipated structure preservation of orbit and skull base; this needs to be determined prior to randomization * Patients may not be receiving investigational agents at time of registration, or at any time while on study and during the 4 weeks preceding enrollment * Patients with a history of allergic rea…