CONCURRENT CHEMOTHERAPY: Patients undergo intensity-modulated radiation therapy (IMRT) or three-dimensional conformal radiotherapy (3D-CRT) once daily (QD) 5 days a week for 6 weeks. Patients receive trametinib orally (PO) QD and carboplatin intravenously (IV) over 30 minutes and paclitaxel IV over 1 hour once weekly. Treatment continues for 6 weeks in the absence of disease progression or unacceptable toxicity. Patients without disease progression after completion of chemoradiation proceed to consolidation chemotherapy.