A question on the limit at infinity

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I appreciate anyone if help me to solve the following problem:

$\sqrt[\pi]{4}=Lim_{n\rightarrow \infty}\,\, \frac{\pi}{2\, tg^{-1}(n)}\, \frac{\pi}{2\, tg^{-1}(n+1)}\cdots \, \frac{\pi}{2\, tg^{-1}(2n)}$