The information is enough to get the function value

Calculus Level 4

f(x+y)=f(x)+f(y)1f(x)f(y)\large f(x+y)=\frac{f(x)+f(y)}{1-f(x)f(y)} The function f(x)f(x) is defined for any value of xx in certain open interval centered at 0, and for any values of xx and yy in that interval the given functional equation is always valid. Additionally, limx0f(x)x=2\displaystyle \lim_{x\to 0} \frac{f(x)}{x}=2.

Find the approximate value of f(π12)f(\frac{\pi}{12}) rounded to the nearest hundredth.

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