Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field = 2 + 4x + 4y across the surface (, theta) = cotheta + theta + (4 - ²), 0 ≤ ≤ 2, 0 ≤ theta ≤ 2 in the direction away from the origin.
The flux of the curl of the field is____
(Type an exact answer, using as needed.)