expressing the given tangent function as a power

Question

Expressing the given tangent function as a power series by determining its coefficients.

Calculate c₀, c₁, c₂, c₃ and c₄ for the power seires that represents f(x) = tan x. Use the first two nonzero terms of the series to approximate the tangent of 1/4 radian. Compare your approximation with the acutal value of the tangent of 1/4 radian as shown on a calculator.