calculus - Prove that $2sum_{k=1}^ncos kθ= frac{sinleft(n+frac12right)θ}{sinfracθ2}-1$

Prove that
$$2\sum_{k=1}^n\cos kθ= \frac{\sin\left(n+\frac12\right)θ}{\sin\fracθ2}-1$$
By using $$e^{iθ}+e^{2iθ}+\cdots+e^{niθ}=\frac{e^{iθ}(1-e^{inθ})}{1-e^{iθ}}$$