If sin⁡−1x≤f(x)≤πetan⁡−1x\sin^{-1}{x}\leq f(x)\leq \pi e^{\tan^{-1}{x}} for 0≤x≤2π0\leq x\leq2\pi, evaluate lim⁡x→0f(x)\lim_{x\to0}{f(x)}.

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