What is the general solution for tan^2(3θ)=1 ?

The general solution for tan^2(3θ)=1 is θ= pi/(12)+(pin)/3 ,θ= pi/4+(pin)/3

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tan^2(3θ)=1

tan^{2} (3 θ) = 1

θ = \frac{π}{12} + \frac{πn}{3}, θ = \frac{π}{4} + \frac{πn}{3}

Solution steps

tan^{2} (3 θ) = 1

Solve by substitution

tan (3 θ) = 1, tan (3 θ) = - 1

tan (3 θ) = 1 : θ = \frac{π}{12} + \frac{πn}{3}

tan (3 θ) = - 1 : θ = \frac{π}{4} + \frac{πn}{3}

Combine all the solutions

θ = \frac{π}{12} + \frac{πn}{3}, θ = \frac{π}{4} + \frac{πn}{3}

tan^{2} (2 θ) - 3 = 0

cos (2 x) = 5 sin^{2} (x) - cos^{2} (x)

3 sec (5 x) - 2 = 0

cot^{2} (x) sec (x) - sec (x) = 2 cot^{2} (x) - 2

5 cot^{2} (x) - 2 csc (x) + 2 = 0

What is the general solution for tan^2(3θ)=1 ?
The general solution for tan^2(3θ)=1 is θ= pi/(12)+(pin)/3 ,θ= pi/4+(pin)/3