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Given an elliptical ranch with dimensions 2 * R units horizontally and 1 unit vertically, a goat is tied to the fence inside the ranch

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 \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
\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

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