Given an elliptical ranch with dimensions $2*$R units horizontally and $1$ unit vertically, a goat is tied to the fence inside the ranch using a leash of length r units. The angle formed between the point of tying and the horizontal axis is $\backslash$theta $.$

To determine the area of grass the goat can graze, the following inputs are provided as shown in the image below:

R half of the horizontal dimension of the ranch,

r the length of the leash, and

$\backslash$theta the angle formed by the point of tying and the horizontal axis.

Write a program that takes these three inputs as floating$-$point numbers on separate lines and prints the total area of grass the goat can graze, rounded to three decimal points