P33. Show that the following nonlinear system has 18 solutions if 0 ≤ α ≤ 2π, 0 ≤ β ≤ 2π, and 0 ≤ γ ≤ 2π.
sin α + 2 cos β + 3 tan γ = 0
2 sin α + 5 cos β + 3 tan γ = 0
−sin α − 5 cos β + 5 tan γ = 0
[Hint: Begin by making the substitutions x = sin α, y = cos β, and z = tan γ .]
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