Functions

Let \(f:( - 1,1) \to R\) be such that \(f(\cos 4\theta ) = {2 \over {2 - {{\sec }^2}\theta }}\) for \(\theta \in \left( {0,{\pi \over 4}} \right) \cup \left( {{\pi \over 4},{\pi \over 2}} \right)\). Then the value(s) of \(f\left( {{1 \over 3}} \right)\) is(are)