Given a function \(\large{f:\mathbb{R}\to\mathbb{R}}\) which satisfies:

\[\large{f(x)+f(y)=f(\frac{x+y}{1-xy})}\] \(\forall x,y \in\mathbb{R}\)

also, \(\large{\lim\limits_{x\to 0}\frac{f(x)}{x}=2}\)

FIND the value of \(\large{f(\frac{1}{\sqrt{3}})=a}\)

ALSO FIND the value of \(\large{f'(1)=b}\)

ENTER YOUR ANSWER AS \(\large{a+b}\)

Answer upto \(\text{5 decimal places}\).

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