Prove that exist $g$ such that $g(x) = f(x) + \alpha\int_0^1g(y)\sin[\cos(x-y)] \mathrm dy$ for all $x\in [0,1]$

Question

Let $\alpha$ be a real constant and $f\in C[0,1]$. Prove that there exist $g\in C[0,1]$ such that $$g(x) = f(x) + \alpha\int_0^1g(y)\sin[\cos(x-y)] \; \mathrm dy , \quad \forall x\in[0,1].$$ I have absolutely no idea how even to start. Can anybody help me ?