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)

Let $$f:(0,1) \to R$$ be defined by $$f(x) = {{b - x} \over {1 - bx}}$$, where be is a constant such that $$0 < b < 1$$. Then