Take the screen center vector v1 and mouse vector v2 and then calculate the vector between the screen center and the mouse courser like this v3 = v2 - v1. Now you use v3 and can calculate the angle with a reference vector. If you want up to be 0° it should be the vector (0,-1) i think. Then take the acos of the normalized vector dot product to find the angle. Something like this (have not tested so hope it is correct):
FMath::Acos(FVector2d::DotProduct(v3.GetSafeNormal(), FVector2d(0,-1)));