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

Suppose a real number $x$ satisfy the equation above.

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

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