trigonometry - If $x costheta+ysintheta=a$ and $xsintheta-ycostheta=b$, then $tantheta=frac{bx+ay}{ax-by}$. (Math Olympiad)

I tried to solve it but I can’t get the answer. Please help me in proving this trig identity:

If
$$x \cos\theta+y\sin\theta=a$$
$$x\sin\theta-y\cos\theta=b$$
then $$\tan\theta=\frac{bx+ay}{ax-by}$$

I've spent many hours trying.
Thanks in advance.