Using all trigonometric functions

Geometry Level 5

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

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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