Find area using double integral and polar coordinates

Find the area enclosed by $$ρ=1+cos(\theta)$$. I can not find the angle of the function to define the limits of the integrals.

This would be the graph of the function:

What I was trying to do, because of the symmetry of the function, was: $$2\int _0^α\int _0^{1+cos\left(\theta \right)}\:ρ\:dρd\theta$$

However, I can't correctly find the angle $$α$$. I would highly appreciate any suggestions.

$$\alpha$$ is the angle at which $$r=1+\cos(\theta) =0$$, therefore $$A= 2\int _0^\pi \int _0^{1+\cos\left(\theta \right)}\:r\:\mathrm dr\mathrm d\theta$$