Question

What best explains why tan(5π/6) does not equal tan(5π/3)?

Answer 1

Let's convert to degrees; easier to think about.

$\tan \dfrac{5\pi}{6} = \tan 150^\circ$

$\tan \dfrac{5\pi}{3} = \tan 300^\circ$

Angles a multiple of 180 degrees or pi radians apart have the same tangent. These are 150 degrees aka 5pi/6 apart so they don't.