If $P(x)$ be a polynomial with real coefficients such that $P(\sin^2 x) = P(\cos^2 x)$, for all $x \in [0, \frac{\pi}{2}]$. Consider the following statements: I. $P(x)$ is an even function. II. $P(x)$ can be expressed as a polynomial in $(2x-1)^2$. III. $P(x)$ is a polynomial of even degree. Then,