Converting from complex fourier series to real

Question

I have a relatively simple fourier series with an $a_k$ value that evaluates to $\dfrac2{j\pi k}$ for all odd values of $k$, and $0$ otherwise, giving the series: $$\sum_{k=-\infty}^{\infty}\frac2{j\pi k}e^{j2\pi f_0kt}$$ We are supposed to give this in real form which supposedly equates to: $$\sum_{k=-\infty}^{\infty}\frac4{\pi k}\sin(2\pi f_0kt)$$ But i'm not sure what steps are taken to get to this solution. I'm aware that the inverse euler's formula $\sin(\theta) = \dfrac1{2j}(e^{j\theta}-e^{-j\theta})$ is supposed to be used but I'm not sure on how exactly I go about evaluating this.