Nonhomogeneous Equations & Resonance · Superchallenge problem

Let $f$ be the sawtooth wave of period $2\pi$ with $f(t)=t$ for $0\le t<2\pi$. The equation $y''+3y'+2y=f(t)$ has exactly one $2\pi$-periodic solution, and that solution has a continuous derivative. Find $y'(0)$ for it.