If $a, b, c$ are direction cosines of a line and $\vec{A} = a\hat{i} + b\hat{j} + c\hat{k}$, $\vec{B} = b\hat{i} + c\hat{j} + a\hat{k}$, then find the maximum angle $\theta$ (in degrees) between $\vec{A}$ & $\vec{B}$ where $\theta \in [0,\pi]$.

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