Compute the determinant. If $a$, $b$, and $c$ are roots of unity. Then what is the value of 
\begin{vmatrix}
e^a & e^{2a} & (e^{3a}-1) \\ 
e^b & e^{2b} & (e^{3b}-1) \\
e^c & e^{2c} & (e^{3c}-1)
\end{vmatrix}
I tried expanding it but the expression becomes unmanageable, is there some kind of simplification I can do?

This is
$$\det\pmatrix{x&x^2&x^3-1\\y&y^2&y^3-1\\z&z^2&z^3-1}
=\det\pmatrix{x&x^2&x^3\\y&y^2&y^3\\z&z^2&z^3}
-\det\pmatrix{x&x^2&1\\y&y^2&1\\z&z^2&1}
$$
for $x=e^a$ etc. Both of these are essentially Vandermonde determinants.
