A Constant Slope Sum at the Focus

The ellipse $\dfrac{x^2}{2} + y^2 = 1$ has right focus $F(1, 0)$. A line through the fixed point $P(2, 0)$ meets the ellipse at $A$ and $B$, and $k_1, k_2$ denote the slopes of $FA$ and $FB$. Prove that $k_1 + k_2$ is constant.