A student attempts to use the small angle to simplify the function

Here is their working:

Suppose $\theta$ is close to $0$. By the small angle approximation,

$$\begin{array}{rl}f(\theta )& =\sin (\cos (\theta ))\\ & \approx \sin (1-\frac{{\theta }^2}{2})\\ & \approx 1-\frac{{\theta }^2}{2}\end{array}$$

Explain why the student's reasoning is invalid.

When $\theta$ is small, what can we say about

?