Let `f:(-1,1)vecR` be such that `f(cos4theta)=2/(2-sec^2theta)` for `theta in ` `(0,pi/4)uu(pi/4,pi/2)` . Then the value(s) of `f(1/3)` is (are) (a)`1-sqrt(3/2)` (b) `1+sqrt(3/2)` (c) `1-sqrt(2/3)` (d) `1+sqrt(2/3)`

Explanation

To solve the problem, we need to find the value of \( f(1/3) \) given that \( f(\cos 4\theta) = \frac{2}{2 - \sec^2\theta} \) for \( \theta \) in the intervals \( (0, \pi/4) \cup (\pi/4, \pi/2) \).

### Step-by-Step Solution:

1. **Set up the equation:**
We start with the equation:
\[
f(\cos 4\theta) = \frac{2}{2 - \sec^2\theta}
...