Let f:(0,2) → R be defined as f(x)= log_2(1+ tan ((π x)/4)). Then, lim_n → ∞ 2/(n)(f(1/n)+f(2/n)+…+f(1)) is equal to \ \ \ \.

Let $\displaystyle f:(0,2) \rightarrow \mathbf{R}$ be defined as $\displaystyle f(x)=\log _2\left(1+\tan \left(\frac{\pi x}{4}\right)\right)$. Then, $\displaystyle \lim _{\mathrm{n} \rightarrow \infty} \frac{2}{\mathrm{n}}\left(f\left(\frac{1}{\mathrm{n}}\right)+f\left(\frac{2}{\mathrm{n}}\right)+\ldots+f(1)\right)$ is equal to \_\_\_\_.