Closed-form expressions of $\sum_{n=1}^\infty \frac{\sin^2(an) e^{-bn^2}}{n^2}$

Question

Does anybody know if there's a closed-form expression of this series? $$\sum_{n=1}^\infty \frac{\sin^2(an) e^{-bn^2}}{n^2}$$ where $a$ and $b$ are strictly positive. It's easy to see that it's absolutely convergent, but I can't really find an expression for it. Thanks in advance!