Trigonometric Tables Are Insufficient!

Geometry Level 4

tan2π16+tan23π16+tan25π16+tan27π16=? \large \tan^{2} \frac{\pi}{16} + \tan^{2} \frac{3\pi}{16} + \tan^{2} \frac{5\pi}{16} + \tan^{2} \frac{7\pi}{16} = \, ?

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