fast way to find eigen vector and eigen value by inspection

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$\begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1& 1 & 0 \\ \end{bmatrix}$

trying to understand how to find Eigen value and vector by inspection for symmetry matrix

$\begin{bmatrix} 0 & 1 & 1 \\ 1 & 0 & 1 \\ 1& 1 & 0 \\ \end{bmatrix}$
as the matrix has trace $0$, which mean sum of eigen values is zero. and sum up each number in row produce 2 which mean 2 is one of Eigen value. beside how can I find another Eigen vector by inspection? and also the other one Eigen value is $-1$ but with geometry multiplicity two. how can I find it using inspection?