Let \( a, b, c \in \mathrm{R} \) be all non-zero and satisfy \( a^{...

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Let \( a, b, c \in \mathrm{R} \) be all non-zero and satisfy \( a^{3}+b^{3}+c^{3}=2 \). If the matrix \(A=\left(\begin{array}{ccc}a & b & c \\ b & c & a \\ c & a & b\end{array}\right)\) satisfies \( A^{\mathrm{T}} \mathrm{A}=\mathrm{I} \), then a value of abc can be:
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