Patients receive WEE1 inhibitor MK-1775 orally (PO) twice daily (BID) on days 2-4, 9-11, and 16-18, and day -7 prior to course 1, day 1 for PD assessment. Patients also receive cisplatin intravenously (IV) on days 1 (or up to two days after last dose of WEE1 inhibitor MK-1775 lead-in is completed), 8 (or 7 days after first chemotherapy dose), and 15, and docetaxel IV on days 1, 8, and 15. Patients experiencing progressive disease undergo surgical resection. Patients not deemed surgically resectable proceed to chemoradiation as clinically indicated. Patients experiencing stable disease or partial response may receive 2 additional courses of treatment every 28 days in the absence of disease progression or unacceptable toxicity.