Show that the complex form of the Fourier series expansion of the periodic function

Is

Using (7.52), obtain the corresponding trigonometric series and check with the series obtained in Example 7.5.
Example 7.5
A periodic function f(t) with period 2π is defined as
f(t) = t 2 (-π t π), f(t) = f(t + 2π)
Obtain a Fourier series expansion for it.