If [tex]A(\cos \theta+\sin \theta, \cos \theta-\sin \theta), B(\cos \theta+\sin \theta, -\cos \theta), C(\sin \theta, \cos \theta-\sin \theta)[/tex], where [tex]\theta \in \mathbb{R}[/tex], are the vertices of a triangle, the locus of the circumcenter is [tex]ax^2 + by^2=c[/tex], where [tex]\gcd(a,b,c)=1[/tex]. What is [tex]a+b+c[/tex]?​