Are sine and cosine missing?

Calculus Level 4

\[\large \int \dfrac{1}{\tan (x) + \cot (x )+ \sec (x) + \csc( x)} \, dx \]

If the indefinite integral above equals to \( \dfrac{\cos (x)}{a} + \dfrac{\sin (x)}{b} + \dfrac{x}{c} \) for constants \(a,b\) and \(c\), what is the value of \(a + b + c\)?

Assume we ignore the arbitrary constant of integration.

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