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

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The function f(x) = |sin x + cos x + tan x + cot x + sec x + csc x| is analyzed to determine its minimum value. Participants discuss the behavior of trigonometric functions and their periodicity, noting that the function is defined for x values where all components are valid. The minimum occurs at specific angles where the sum of the trigonometric functions reaches its lowest point. Various methods, including calculus and numerical approximation, are suggested to find the minimum value. Ultimately, the discussion emphasizes the importance of understanding the properties of trigonometric functions in solving such problems.
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let $f(x)=\left |sin\, x+cos\, x+tan\, x+cot\, x+sec\, x +csc\, x \right |$

please find minimum $f(x)$
 
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This problem has previously been posted and solved here:

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

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