\(ABCD\) is a tetrahedron with a length of \( AB = 3, AC = 8, AD = 6, BC = 7, BD = 5\) and \(CD = 4\). If \(n\) is the distance between the midpoint \(AB\) and \(CD\), then what is the value of \(n^2 \)?

The brown shaded area is the surface area.

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