A Challenging Problem of Tetrahedron by H.C.R

Geometry Level 5

The diagram above shows a tetrahedron with vertices \(A,B,C,D\). If the angles between the lateral edges \(AC\) & \(AD\), \(AB\) & \(AD\) and \(AB\) & \(AC\) meeting at the vertex \(A\) are \(\alpha =40^\circ, \beta=70^\circ , \gamma=85^\circ \) respectively, then calculate the correct value (up to three decimal points) of the solid angle (in Ste-radian) subtended by triangular face \(BCD\) at the vertex \(A\).

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