Let $\mathbf{F} = (2 x, 2 y , 2 x + 2 z)$. Use Stokes' theorem to evaluate the integral of $\mathbf{F}$ around the curve consisting of the straight lines joining the points (1,0,1), (0,1,0) and (0,0,1). In particular, compute the unit normal vector and the curl of $\mathbf{F}$ as well as the value of the integral:
$\mathbf{n} = ($,, $)$ (the unit normal vector)
$\nabla \times \mathbf{F} = ($,, $)$
The value of the integral is .