trigonometry - Use $e^{ia}+e^{ib}$ to show that $y(t)=2Acos(frac{delta}{2}t-frac{phi_1 -phi_2}{2})sin((omega+frac{delta}{2})t+frac{phi_1 +phi_2}{2})$

One guitarist causes an oscillation given by
$$y_1(t)=A\sin({\omega}t+\phi_1)$$

Another guitarist causes an oscillation given by
$$y_2(t)=A\sin({(\omega+\delta)}t+\phi_2)$$

Furthermore,
$$y(t)=y_1(t)+y_2(t)$$

Given formula (1)
$$e^{ia}+e^{ib}=2e^{i\frac{(a+b)}{2}}\cos(\frac{a-b}{2})$$

Formula (1) should be used to show
$$y(t)=2A\cos(\frac{\delta}{2}t-\frac{\phi_1 -\phi_2}{2})\sin((\omega+\frac{\delta}{2})t+\frac{\phi_1 +\phi_2}{2})$$
I've attempted adding $y_1(t)$ and $y_2(t)$, hoping that something useful would drop out. However, this becomes quite messy after using angle sum identities and I can't make sense of it. I've considered double angle formulae, product-to-sum, sum-to-product formulae. What is a good approach to solving this problem?