Proving that $d\theta_{fX}=df.\theta_X+\theta_X.df+d(f\theta_X)$

Question

Let $\theta_X$ be a $1$-form. "Riemannian Geometry" by Peter Petersen, on pg 25, has the following formula:

$$d\theta_{fX}=df.\theta_X+\theta_X.df+d(f\theta_X)$$

1. What does the dot product of two $1$-forms mean? What does $df.\theta_X$ mean?

2. Where does the formula given above come from?