How to Find the Minimum of f(x) in an Absolute Value Trigonometric Function?

[Albert1]

let $f(x)=\left |sin\, x+cos\, x+tan\, x+cot\, x+sec\, x +csc\, x \right |$

please find minimum $f(x)$

 

[MarkFL]

Spoiler

This problem has previously been posted and solved here:

http://mathhelpboards.com/challenge-questions-puzzles-28/minimize-trigonometric-expression-4330.html