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

the problem is:

Evaluate on E xyz dV where E lies between the spheres =2 and =4 and above the cone = /3.

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

1/4 sin^4 from 0 to * 1/2sin^2 from 0 to 2 * 1/6 ^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 )/15