The values of 0 ≤ θ ≤ 2π are π/6, π/4, π/3, π/2, 2π/3, 3π/4, 5π/6, π, 7π/6, 5π/4, 4π/3, 5π/3, 7π/4 and 11π/6. It can be inputted into trigonometric functions. Tangent is sine over cosine. Since sine and cosine are periodic, then tangent has to be, as well.–π to –π/2: The tangent will be zero wherever its numerator (the sine) is zero. This happens at 0, π, 2π, 3π, etc, and at –π, –2π, –3π, etc. The tangent will be undefined wherever its denominator (the cosine) is zero. A zero in the denominator means you'll have a vertical asymptote. So the tangent will have vertical asymptotes wherever the cosine is zero