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

(cosγ)x+y+(cosα)z=0,(\cos \gamma) x + y + (\cos \alpha) z = 0,

(cosβ)x+(cosα)y+z=0(\cos \beta) x + (\cos \alpha) y + z = 0

has: