Calculating the volume of $(x-z)^2+(y-z)^2 \le \sin^2(z) $

Question

I am trying to calculate the volume of $(x-z)^2+(y-z)^2 \le \sin^2(z) $ and $0 \le z \le \pi $. I am having trouble parameterising the equation and setting the bounds for the parameters. I think the $-z$ in the equation is just rescaling the object so it does not affect the volume. I have set the volume integral as $$ \pi \int_{0}^{\pi}\sin^2(z) dz$$ and found the volume as $\frac{\pi^2}{2} $. Is this the correct answer or is my calculation wrong? Thank you very much!