# Tangents of nonstandard angles?

Geometry Level 4

$\sqrt3 \left(\frac{1}{\sqrt3}+\tan1^\circ\right)\left(\frac{1}{\sqrt3}+\tan2^\circ\right)\cdots\left(\frac{1}{\sqrt3}+\tan58^\circ\right)\left(\frac{1}{\sqrt3}+\tan59^\circ\right)$

The above product can be written as $$\dfrac{a^{b}}{c^{d}}$$, where $$a, c$$ are prime numbers. Then find $$a+b+c+d$$ upto 2 decimal places.

Bonus:

Try to generalize (I think you'll get what I'm saying once you solve the problem).

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