Uniform Mixing in a 3x3 Guessing Game

Consider the zero-sum matrix with payoff $+1$ on the diagonal and $-1$ off the diagonal: \[ \begin{pmatrix} 1 & -1 & -1 \\ -1 & 1 & -1 \\ -1 & -1 & 1 \end{pmatrix}. \] Find the mixed equilibrium and the value.