Question: How can find dihedral angle of two halfplanes?

I see here 
https://mathematica.stackexchange.com/questions/306634/how-can-i-use-dihedralangle-to-get-correct-result/306638?noredirect=1#comment751373_306638

Let $S.ABCD$ be a pyramid, $ABCD$ is a square with $AB = 1$. The line $SA$ perpendicular to the plane $ABC$. 

Calculate dihedral angle of two halfplanes `SBC` and `SCD` if: $SA = 1$, $SA = \dfrac{\sqrt{2}}{2}$.  I tried
restart;
with(Student:-MultivariateCalculus);
a := 1;
h := 1;
pA := [0, 0, 0];
pB := [a, 0, 0];
pC := [a, a, 0];
pD := [0, a, 0];
pS := [0, 0, h];

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