1.
If α+β+γ=2π\alpha + \beta + \gamma = 2\pi, then the system of equations
x+(cos⁡γ)y+(cos⁡β)z=0,x + (\cos \gamma) y + (\cos \beta) z = 0,

(cos⁡γ)x+y+(cos⁡α)z=0,(\cos \gamma) x + y + (\cos \alpha) z = 0,

(cos⁡β)x+(cos⁡α)y+z=0(\cos \beta) x + (\cos \alpha) y + z = 0

has: