Expressing $\sum_{k=1}^3(A_k\cos(x-\alpha_k)-C_k)^2$ in the form $A\cos(x-\alpha)+B$

Question

I have the following sum $$f(x) = \sum_{k=1}^3 (A_k \cos(x - \alpha_k) - C_k)^2$$ which I want to bring into the form $$f(x) = A\cos(x - \alpha) + B$$ I know I can rewrite with the squares the entire expression to $$f(x) = A^*\cos^2(x - \alpha_k) + B^*\cos(x - \alpha_k) + C^*$$ with constants, $A^*, B^*, C^*$, but I'm unsure how they are connected to the start equation. How could I solve this?

I want to bring it into the form described as part of a proof.