5. Let C be the union of the four curves $y = \sqrt{1 - x^2} + 1$, $y = -\sqrt{1 - x^2} - 1$,
$x = \sqrt{1 - y^2} + 1$, and $x = -\sqrt{1 - y^2} - 1$ with counterclockwise orientation. Evaluate $\oint_C (\sin(2x) + \arctan y) dy - 4y \sin^2 x \, dx.$