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

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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
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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