How does one parameterize $x^2 + xy + y^2 = \frac{1}{2}$? 
Parameterize the curve $C$ that intersects the surface
  $x^2+y^2+z^2=1$ and the plane $x+y+z=0$.

I have this replacing equations:
$$ x^2+y^2+(-x-y)^2=1$$
and clearing have the following:
$$ x^2+xy+y^2=1/2$$
which it is the equation of an ellipse but I find it difficult parameterization values
Any advice will be of much help, thanks in advance


Let 
\begin{equation}
x=\sqrt{\frac{2}{3}}\sin(t)
\end{equation}
\begin{equation}
y=\sqrt{\frac{2}{3}}\sin\left(t+\frac{2\pi}{3}\right)
\end{equation}
\begin{equation}
z=\sqrt{\frac{2}{3}}\sin\left(t-\frac{2\pi}{3}\right)
\end{equation}
Then $x+y+z=0$ and $x^2+y^2+z^2=1$
