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

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

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tan^2(2x)= 1/3

tan^{2} (2 x) = \frac{1}{3}

x = \frac{π}{12} + \frac{πn}{2}, x = - \frac{π}{12} + \frac{πn}{2}

Solution steps

tan^{2} (2 x) = \frac{1}{3}

Solve by substitution

tan (2 x) = \frac{1}{3}, tan (2 x) = - \frac{1}{3}

tan (2 x) = \frac{1}{3} : x = \frac{π}{12} + \frac{πn}{2}

tan (2 x) = - \frac{1}{3} : x = - \frac{π}{12} + \frac{πn}{2}

Combine all the solutions

x = \frac{π}{12} + \frac{πn}{2}, x = - \frac{π}{12} + \frac{πn}{2}

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