Finding the Integral of csc^2x: What to Do When Tanx is Undefined at pi/6?

[Eshi]

Homework Statement

find the integral of (cscx)² between pie/6 to pie/2

The Attempt at a Solution

cot²x = 1 / sin²x * cos²x / cos²x
which becomes..
tan²x * sec²x
then i substituted u for tan x, and turned the integral into..
u²du = u³ / 3
which is..
tan³x / 3 between pie/6 and pie/2.

However, tan is undefined at pie/6! what do i do?

 

[Bohrok]

cot²x = 1 / sin²x * cos²x / cos²x
which becomes..
tan²x * sec²x

No, that last line should be cot²x * sec²x, and the cot in the first line should be csc.

However, tan is undefined at pie/6! what do i do?

That's not true; it is defined at $\pi$/6. What is sin$\pi$/6 and cos$\pi$/6? Put sine over cosine.