# 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).