Let y = y(x) be the solution of the differential equation x tan(y/x) dy = [y tan(y/x) - x]dx, -1 ≤ 1, y(1/2) = π/6. Then the area of the region bounded by the curves x = 0, x = 1/√2 and y = y(x) in the upper half plane is:

(1) 1/8(π - 1)
(2) 1/12(π - 3)
(3) 1/4(π - 2)
(4) 1/6(π - 1)