Show that the following nonlinear system has 18 solutions if 0 2, 0

Show that the following nonlinear system has 18 solutions if 0 ≤ α ≤ 2π, 0 ≤ β ≤ 2π, and 0 ≤ γ < 2π.
2sin α - cos β + 3 tan γ = 3
4sin α - 2 cos β + 2 tan γ = 2
6sin α - 3 cos β + tan γ = 9