The flat angles of the triangular corner are 45, 45 and 60 degrees. Find the dihedral that is opposite

The flat angles of the triangular corner are 45, 45 and 60 degrees. Find the dihedral that is opposite the planar angle of 60 degrees.

Let α, β, γ be plane angles of a trihedral angle, they correspond to dihedral angles A, B, C.
We have angles α = 45˚, β = 45˚, γ = 60˚.
According to the first theorem of cosines for a trihedral angle, we have:
cos γ = cos α * cos β + sin α * sin β * cos C.
Take cos C out of this expression:
cos C = (cos γ – cos α * cos β) / (sin α * sin β).
cos C = (cos 60 – cos 45 * cos 45) / (sin 45 * sin 45) = ((1/2) – (√2 / 2) ²) / (√3 / 2) ² = (1/2 -1/2) / (√3 / 2) ² = 0.
This cosine value corresponds to an angle of 90˚.
Answer: a dihedral angle opposite a flat angle of 60˚ = 90˚.