algebra precalculus - Find $cos2theta+cos2phi$, given $sintheta + sinphi = a$ and $costheta+cosphi = b$

If

$$\sin\theta + \sin\phi = a \quad\text{and}\quad \cos\theta+\cos\phi = b$$

then find the value of

$$\cos2\theta+\cos2\phi$$

My attempt:

Squaring both sides of the second given equation:

$$\cos^2\theta+ \cos^2\phi + 2\cos\theta\cos\phi= b^2$$

Multiplying by 2 and subtracting 2 from both sides we obtain,

$$\cos2\theta+ \cos2\phi = 2b^2-2 - 4\cos\theta\cos\phi$$

How do I continue from here?

PS: I also found the value of $\sin(\theta+\phi)= \dfrac{2ab}{a^2+b^2}$

Edit: I had also tried to use $\cos2\theta + \cos2\phi= \cos(\theta+\phi)\cos(\theta-\phi)$ but that didn't seem to be of much use