Given a right-angled triangle with integer sides, the smaller angle formed by the two medians drawn on the the two perpendicular sides is denoted by $\theta$.

Let $f(\alpha ,L)$ denote the sum of the sides of the right-angled triangle minimizing the absolute difference between $\theta$ and $\alpha$ among all right-angled triangles with integer sides and hypotenuse not exceeding $L$.
If more than one triangle attains the minimum value, the triangle with the maximum area is chosen. All angles in this problem are measured in degrees.

For example, $f(30,{10}^2)=198$ and $f(10,{10}^6)=1600158$.

Define $F(N,L)=\sum _{n=1}^{N}f(\sqrt[3]{n},L)$.
You are given $F(10,{10}^6)=16684370$.

Find $F(45000,{10}^{10})$.