θ \theta is increasing

Geometry Level 3

If θ = π 4 n \large {\theta=\frac{\pi}{4n}} where n N n\in\mathbb N . Then find the value of it:

t a n θ t a n 2 θ t a n 3 θ . . . . . . . . . . . . . t a n ( 2 n 1 ) θ = ? ? \large tan\theta\cdot tan2\theta\cdot tan3\theta .............tan(2n-1)\theta=??

None of them 0 3 \sqrt3 4n 1

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