Calculate the line integral $\int_C \mathbf{F} \cdot d\mathbf{r}$ for $\mathbf{F} = \langle 2x, 2y, 2z \rangle$ where $C$ is the path $\mathbf{r}(t) = \langle \cos t, \sin t, t \rangle$ for $0 \le t \le \pi$.