I have 2 random variables X and Y with the distribution table:

$$
 X,Y{\raise.17ex\hbox{$\scriptstyle\mathtt{\sim}$}} \begin{pmatrix}
 -1 & 0 & 1 \\
 0.25 & 0.5 & 0.25 \\
 \end{pmatrix}
$$

I have to find
$$
 P(X+Y<0)
$$

Now I don't have an idea on how to find the distribution table of X+Y if that's necessary.

For now I know that 
$$
 E(X+Y)= E(X)+E(Y) = 0 
$$
and
$$
 V(X) = 0.5
$$

So

$$
 P(X+Y<0) = P(X=-1,Y=-1)+P(X=-1,Y=0)+P(X=0,Y=-1)
$$

Can you please point me in the right direction from what should I find now?
My thoughts where that I need to find the distribution table of X+Y in order to find those 3 probabilities, but I don't know how to do it.

Thanks!