Find the value of the Determinant If $a^2+b^2+c^2+ab+bc+ca \le 0\quad \forall a, b, c\in\mathbb{R}$, 
then find the value of the determinant 
$$ \begin{vmatrix}
        (a+b+2)^2 & a^2+b^2 & 1 \\
        1 & (b+c+2)^2 & b^2+c^2 \\
        c^2+a^2 & 1 & (c+a+2)^2 \\
        \end{vmatrix}$$
I tried expanding the whole squares and using the identity $(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$, but the result is incorrect. How should I evaluate this ?

Hint
$$\dfrac{1}{2}[(a+b)^2+(b+c)^2+(a+c)^2]=a^2+b^2+c^2+ab+ac+bc\le 0$$
so we have
$$a=-b,b=-c,c=-a\Longrightarrow  a=b=c=0$$
