Let $\mathbf{F}(x_1, x_2, x_3) = (2x_1 + x_2) \mathbf{i} + (2x_2 - x_1) \mathbf{j}$, and $C$ be the helix $\mathbf{C}(t) = \langle \cos t, \sin t, t \rangle$, $t \in [0, 3\pi]$, along with the long segment from $(-1, 0, 3\pi)$ to $(1, 0, 0)$. Evaluate the circulation $\oint_C \mathbf{F} \cdot d\mathbf{r}$.