Let $r(a,b)$ be a rational number depending on $a,b$ and nonnegative. For every $b$ there is an $a$ such that $r(a,b)$ is not $0$.
Let $C(a,b)$ be a squarefree positive integer depending on $b$ and different for every $b$.
Consider for positive integers $I,J$ :
$$ S_J = \sum_{j=1}^J \sum_{i=1}^I \arcsin\left( r(i,j) \sqrt {C(i,j)} \right) $$
Where $ r(i,j) \sqrt C(i,j) $ is always smaller than $1$.
Conjecture G
For $J>2$
$$ S_J \neq 2 \pi $$
Is this true ??