Two distinct lines pass through the center of three concentric circles of radii $3,2,1$. The area of the shaded region in the diagram is $\frac35$ of the area of the unshaded region. What is the radian measure of the acute angle formed by the two lines?

1. If the acute angle is $\alpha$, the total shaded area is $3\pi+3\alpha$ (out of the whole disk's $9\pi$).
2. If shaded:unshaded$=p:q$, then $\dfrac{3\pi+3\alpha}{9\pi}=\dfrac{p}{p+q}$, giving $\alpha=\dfrac{\pi(2p-q)}{p+q}$.
3. With $p=3,q=5$: $\alpha=\dfrac{\pi(6-5)}8=\boxed{\dfrac{\pi}8}$.