solve trigonometric function using other given equation

Question

we have two equations:

x+y+z = 1 and

cos(x) = cos(y) = cos(z) = #(consider it as lambda)

how can i find the value of x,y and z?

Answer 1

cos x = cos y = cos z ⇒ x = y = z

If x + y + z = 1, and x = y = z, then x = y = z = 1/3