Are sine and cosine missing?

$\Rightarrow \text{I} = \int \dfrac{1}{\tan x + \cot x + \sec x + \csc x} \text{dx}$

$\Rightarrow \text{I} = \int \dfrac{ \sin x \cos x}{\sin^2 x + \sin x + \cos x + \cos^2 x}\text{dx}$

$\text{Multiplying and divide by 2}$ $\Rightarrow \text{I} = \dfrac{1}{2} \int \dfrac{(\sin x + \cos x)^2 - 1}{1 + \sin x + \cos x} \text{dx}$

$\Rightarrow \text{I} = \dfrac{1}{2} \int \sin x + \cos x - 1$

$\Rightarrow \text{I} = \dfrac{\cos x}{-2} + \dfrac{\sin x}{2} + \dfrac{x}{-2} + \text{constant}$

$\therefore \text{a + b + c} = -2 + 2 - 2 = \boxed{\color{#3D99F6}{-2}}$

If you add the numbers, you will get -2. The last part of my solution didn't get captured in the picture, but the work is there.