Let `f:(-1,1)toR` 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 \( f\left(\frac{1}{3}\right) \) given the function \( f(\cos 4\theta) = \frac{2}{2 - \sec^2 \theta} \) for \( \theta \in (0, \frac{\pi}{4}) \cup (\frac{\pi}{4}, \frac{\pi}{2}) \).

### Step 1: Set up the equation
We start with the equation:
\[ \cos 4\theta = \frac{1}{3} \]
We know that:
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