Draw the graph of `f(x) = sec x + "cosec " x, x in (0, 2pi) - {pi//2, pi, 3pi//2}`
Also find the values of 'a' for which the equation `sec x + "cosec " x = a` has two distinct root and four distinct roots.

Explanation

To solve the problem step by step, we will first draw the graph of the function \( f(x) = \sec x + \csc x \) for \( x \in (0, 2\pi) \setminus \{\frac{\pi}{2}, \pi, \frac{3\pi}{2}\} \) and then find the values of \( a \) for which the equation \( \sec x + \csc x = a \) has two distinct roots and four distinct roots.

### Step 1: Identify the Domain
The function \( f(x) = \sec x + \csc x \) is undefined at \( x = \frac{\pi}{2}, \pi, \frac{3\pi}{2} \) because \( \sec x \) and \( \csc x \) approach infinity at these points. Thus, we will consider the intervals:
- \( (0, \frac{\pi}{2}) \)
- \( (\frac{\pi}{2}, \pi) \)
- \( (\pi, \frac{3\pi}{2}) \)
- \( (\frac{3\pi}{2}, 2\pi) \)
...