Find the work done by the force field $\mathbf{F}(x, y, z) = 2x\mathbf i + 2y\mathbf j + 6\mathbf k$ on a particle that moves along the helix $\mathbf{r}(t) = 2 \cos(t)\mathbf i + 2 \sin(t)\mathbf j + 5t\mathbf k, 0 \leq t \leq 2\pi$.