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Let $f : (0, 2) \to \mathbb{R}$ be defined as $f(x) = \log_2\left(1 + \tan\left(\dfrac{\pi x}{4}\right)\right)$.
Then, $\lim_{n \to \infty} \dfrac{2}{n}\left(f\left(\dfrac{1}{n}\right) + f\left(\dfrac{2}{n}\right) + \cdots + f(1)\right)$ is equal to ______.
BETA
