I am given an elliptic curve with homogeneous equation $X^3+Y^3+Z^3=0$ over a field K and I am asked to find the Weierstrass normal form. 

I started by noticing that the point $(1,-1,0)$ is in the curve. Then, I find the tangent line at the point:
$$\frac{\partial F}{\partial X}(X-1)+\frac{\partial F}{\partial Y}(Y+1)+\frac{\partial F}{\partial Z}(Z-0) = 0$$
to get
$$Y=-X$$ 
But when I plug this in the initial equation I get $$Z^3 = 0$$ and here I stopped the process because these seem strange.