Are sine and cosine missing?

Calculus Level 5

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

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.