Solve the given equation.

tan^4(πœƒ) βˆ’ 34 tan^2(πœƒ) + 225 = 0

c'mon, this is just a quadratic equation in tan^2ΞΈ

(tan^2ΞΈ-9)(tan^2ΞΈ-25) = 0
tanΞΈ = Β±3
tanΞΈ = Β±5
so it looks like each case has a solution in each quadrant.