# 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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