I need some help with a triple integral problem that I keep getting wrong in the last step somehow.

the problem is:

Evaluate $\displaystyle \int\int\int$ on E xyz dV where E lies between the spheres $\displaystyle \rho$=2 and $\displaystyle \rho$=4 and above the cone $\displaystyle \phi$=$\displaystyle \pi$/3.

There work I've done so far is set up the integral integrated it and got:

1/4 sin^4$\displaystyle \phi$ from 0 to $\displaystyle \pi$ * 1/2sin^2$\displaystyle \theta$ from 0 to 2$\displaystyle \pi$ * 1/6 $\displaystyle \rho$^6 from 2 to 4.

I get that the middle term should be zero, but for some reason my prof gives the answer to be

(1562$\displaystyle \pi$)/15