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 \(\vec{b}.\)