Please reason step by step, and put your final answer within \boxed{}.
If the vector $\vec{a} + 3\vec{b}$ is perpendicular to the vector $7\vec{a} - 5\vec{b}$, and the vector $\vec{a} - 4\vec{b}$ is perpendicular to the vector $7\vec{a} - 2\vec{b}$, then the angle between the vectors $\vec{a}$ and $\vec{b}$ is $\qquad$.
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