Using all trigonometric functions

Geometry Level 5

sin(x)+cos(x)+tan(x)+csc(x)+sec(x)+cot(x)=7 \large \sin(x) + \cos(x) + \tan(x) + \csc(x) + \sec(x) + \cot(x) = 7

Suppose a real number xx satisfy the equation above.

And for positive constants a,b,ca,b,c, we have sin(2x)=abc\sin(2x) = a - b \sqrt c with cc square-free. Find the value of ab+2ca-b+2c.

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