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These AITTSs are expressed as $\\rho _{aiso}=p\\left\\vert \\psi _{\\left( \\theta,\\phi \\right) }\\right\\rangle \\left\\langle \\psi _{\\left( \\theta ,\\phi \\right)}\\right\\vert +(1-p)\\frac{1_{9}}{9}$ with $\\left\\vert \\psi _{\\left( \\theta,\\phi \\right) }\\right\\rangle =\\sin \\theta \\cos \\phi \\left\\vert00\\right\\rangle +\\sin \\theta \\sin \\phi \\left\\vert 11\\right\\rangle +\\cos\\theta \\left\\vert 22\\right\\rangle $ and $1_{9}=\\sum_{j,k=0}^{2}\\left\\vert jk\\right\\rangle \\left\\langle jk\\right\\vert $. 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