If \( \left(\cos ^{-1}(x)\right)^{2}+\left(\cos ^{-1} y\right)^{2}+\left(\cos ^{-1} z\right)^{2}....

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If \( \left(\cos ^{-1}(x)\right)^{2}+\left(\cos ^{-1} y\right)^{2}+\left(\cos ^{-1} z\right)^{2}=3 \pi^{2} \), then find the value of \( x^{2}+y^{2}+z^{2} \).
\( \mathrm{P} \)
(1) 1
(2) 0
(3) 3
(4) None of these


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