complex numbers - Find the real and imaginary parts

Find the real and imaginary parts of : $$\frac {e^{iθ}} {1-λe^{iΦ}}$$

Here i=iota

I have used $e^{iθ} = \cos θ +i \sin θ$ but I am not able to separate real and imaginary parts. I am not getting any clue how to proceed.

The answer given in my textbook:
Real: $\frac {cos θ - λ cos(θ-Φ)} {1-2λ cos Φ + λ^2}$

Imaginary: $\frac {sin θ - λ sin(θ-Φ)} {1-2λ cos Φ + λ^2}$

Thank you