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If \(\vec{a}, \vec{b}\) are unit vectors such that the vector \(\vec{a}+3\,\vec{b}\) is perpendicular to \(7\,\vec{a}-5\,\vec{b}\) and \(\vec{a}-4\,\vec{b}\) is perpendicular to \(7\,\vec{a}-2\,\vec{b},\) then find the angle between \(\vec{a}\) and \(\vec{b}.\)

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Let angle between \(\vec{a}\) and \(\vec{b}\) be \(\theta\)

Also, given that \((\vec{a} - 4\vec{b}) \perp (7\vec{a} - 2\vec{b})\)

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