Solve in radians: tanθ=1.θ=π4+2kπ or θ=−π4+2kπ where k∈Z.θ=π4+kπ where k∈Z.θ=−π4+kπ where k∈Z.

The given equation is tanθ = 1.

The solutions to this equation are the angles for which the tangent function equals 1.

The tangent function equals 1 at π/4 and -π/4 (in the first and third quadrants, respectively) in the unit circle.

However, the tangent function is periodic with a period of π, so we must also include all angles that are coterminal with π/4 and -π/4.

This gives us the general solutions:

θ = π/4 + kπ and θ = -π/4 + kπ, where k is any integer.

So, the solutions to the equation tanθ = 1 are all angles that are coterminal with π/4 and -π/4.