5 A regular tetrahedron has vertices at the points $$A \left( 0,0 , \frac { 2 } { 3 } \sqrt { 6 } \right) , \quad B \left( \frac { 2 } { 3 } \sqrt { 3 } , 0,0 \right) , \quad C \left( - \frac { 1 } { 3 } \sqrt { 3 } , 1,0 \right) , \quad D \left( - \frac { 1 } { 3 } \sqrt { 3 } , - 1,0 \right) .$$

1. Obtain the equation of the face \(A B C\) in the form $$x + \sqrt { 3 } y + \left( \frac { 1 } { 2 } \sqrt { 2 } \right) z = \frac { 2 } { 3 } \sqrt { 3 }$$ (Answers which only verify the given equation will not receive full credit.)
2. Give a geometrical reason why the equation of the face \(A B D\) can be expressed as $$x - \sqrt { 3 } y + \left( \frac { 1 } { 2 } \sqrt { 2 } \right) z = \frac { 2 } { 3 } \sqrt { 3 }$$
3. Hence find the cosine of the angle between two faces of the tetrahedron.