To find the critical points, we need to find where the derivative of $f$ is equal to zero or undefined.
The derivative of $f$ is given by:
$$f'(t) = 1 - \frac{1}{2}\csc^2\left(\frac{t}{2}\right)$$
To find where $f'(t) = 0$, we need to solve the equation:
$$1 -
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