Let $\mathbf{F}(x,y) = \langle -\frac{y}{x^2+y^2}, \frac{x}{x^2+y^2} \rangle$ for $(x,y) \neq (0,0)$. Evaluate the line integral $\oint_C \mathbf{F} \cdot d\mathbf{r}$ where $C$ is the non-standard closed curve parameterized in polar coordinates by $r(\theta) = 2 + \cos(3\theta)$ for $0 \le \theta \le 2\pi$, oriented counterclockwise.