Let α and β be the roots of the equation x^2+x+1=0. Then for y ≠ 0 in R, |y+1, α, β; α, y+β, 1; β, 1, y+α| is equal to:

Let $\displaystyle \alpha$ and $\displaystyle \beta$ be the roots of the equation $\displaystyle x^2+x+1=0$. Then for $\displaystyle y \neq 0$ in $\displaystyle \mathbf{R}$, $$\left|\begin{array}{ccc} y+1 & \alpha & \beta \\ \alpha & y+\beta & 1 \\ \beta & 1 & y+\alpha \end{array}\right| \text { is equal to : } $$