What is the coefficient of $\displaystyle x^4$ in the series expansion of $\displaystyle (1+x+x^2)^{-4}$?

This would be easy if it were just $\displaystyle (1+x^2)^{-4}$;however, I don't know what to do with the three terms.

Normally I would find the coefficient of such a problem as follows:

$\displaystyle x^4$ in $\displaystyle (1+x^2)^{-4}$

= $\displaystyle -4\choose{i}$$\displaystyle (x^2)^i$

$\displaystyle 2i = 4$

$\displaystyle i = 2$

$\displaystyle 5\choose{2}$$\displaystyle (1)^2$

$\displaystyle = 10$