Coefficients of series equation

Question

Is there a way to compute the coefficients $a_k$ in series of the form $\sum\limits_{k=1}^{\infty}a_k \sin(ka) = b$ and $\sum\limits_{k=1}^{\infty}a_k \sin(ka) k = b$ for fixed constants $a,b\in\mathbb{R}$? I thought about Fourier series of course but without dependence of $x$ of the sin term I am stuck... Thanks.