Three concentric circles centered at O have radii of 1, 2, and 3. Points B and C lie on the largest circle. The region between the two smaller circles is shaded, as is the portion of the region between the two larger circles bounded by the central angle \angle BOC, as shown in the figure below. Suppose the shaded and unshaded regions are equal in area. What is the measure of \angle BOC in degrees?
Answer Choices
A. 108
B. 120
C. 135
D. 144
E. 150