The famous Indian astronomer, Aryabhata, approximated the value of \(\pi\) as \( 3.1416 \) and then expressed it as a continued fraction of the form

\[ \large a+\frac{1}{b+\frac{1}{c+\frac{1}{d}}}, \]

where \( a,b,c,d \) are positive integers. Find \( a+b+c+d\).

\(\)

**Details and Assumptions:**

- Use the approximation \( \pi = 3.1416 \).

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