Partial Derivatives & the Gradient · Superchallenge problem

Let $A = (-1, 0)$ and $B = (1, 0)$. For a point $P = (x,y)$ with $y > 0$, let $\theta(x,y) = \angle APB$ be the angle at which the segment $AB$ is seen from $P$. Find $\lvert\nabla\theta\rvert$ at $P = (1, 2)$.