The quadratic pinned-endpoint angle conjecture

Let $A$ be a pinned point in a configuration of $n$ points in general position in $\mathbb R^2$ or $\mathbb R^3$, where general position means no three points are collinear and no four points lie on a circle. Count the distinct angles formed by triples of points in which $A$ is one of the endpoints. Quadratic pinned-endpoint angle conjecture. For any such configuration, the number of distinct angles is $\Theta(n^2)$. The source proves a lower bound of $\Omega(\sqrt n)$ in three dimensions and notes that no nontrivial upper bound beyond the trivial $O(n^2)$ count is known for the pinned-endpoint variant.