Let f : (0, 2) $\to$ R be defined as f(x) = log₂$\left( {1 + \tan \left( {{{\pi x} \over 4}} \right)} \right)$. Then, $\mathop {\lim }\limits_{n \to \infty } {2 \over n}\left( {f\left( {{1 \over n}} \right) + f\left( {{2 \over n}} \right) + ... + f(1)} \right)$ is equal to ___________.