Take the inverse tangent of both sides of the equation to extract from inside the tangent.

Evaluate .

The tangent function is negative in the second and fourth quadrants. To find the second solution, subtract the reference angle from to find the solution in the third quadrant.

Simplify .

Multiply by .

Subtract from .

Add to .

The resulting angle of is positive and coterminal with .

The period of the function can be calculated using .

Replace with in the formula for period.

Solve the equation.

The absolute value is the distance between a number and zero. The distance between and is .

Divide by .

Add to to find the positive angle.

Replace with decimal approximation.

Subtract from .

List the new angles.

The period of the function is so values will repeat every radians in both directions.

, for any integer

Exclude the solutions that do not make true.

, for any integer

Solve for x tan(x)=-2