Take the inverse tangent of both sides of the equation to extract <math><mstyle displaystyle="true"><mi>x</mi></mstyle></math> from inside the tangent.

Evaluate <math><mstyle displaystyle="true"><mi>arctan</mi><mrow><mo>(</mo><mfrac><mrow><mn>5</mn></mrow><mrow><mn>6</mn></mrow></mfrac><mo>)</mo></mrow></mstyle></math> .

The tangent function is positive in the first and third quadrants. To find the second solution, add the reference angle from <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> to find the solution in the fourth quadrant.

Remove the parentheses around the expression <math><mstyle displaystyle="true"><mn>3.14159265</mn></mstyle></math> .

Add <math><mstyle displaystyle="true"><mn>3.14159265</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>0.69473827</mn></mstyle></math> .

The period of the function can be calculated using <math><mstyle displaystyle="true"><mfrac><mrow><mi>π</mi></mrow><mrow><mrow><mo>|</mo><mi>b</mi><mo>|</mo></mrow></mrow></mfrac></mstyle></math> .

Replace <math><mstyle displaystyle="true"><mi>b</mi></mstyle></math> with <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> in the formula for period.

Solve the equation.

The absolute value is the distance between a number and zero. The distance between <math><mstyle displaystyle="true"><mn>0</mn></mstyle></math> and <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> is <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

Divide <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> by <math><mstyle displaystyle="true"><mn>1</mn></mstyle></math> .

The period of the <math><mstyle displaystyle="true"><mi>tan</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mstyle></math> function is <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> so values will repeat every <math><mstyle displaystyle="true"><mi>π</mi></mstyle></math> radians in both directions.

Consolidate the answers.

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