\( -\frac{\pi}{2}<\theta \leq \frac{\pi}{2} \). Find the value of \( \theta \) in radians. \( \cot (\theta)=0 \) Write your answer in simplified, rationalized form. Do not round. \( \theta=\square \)

The equation \( \cot(\theta) = 0 \) indicates that the cosine of \( \theta \) is zero while the sine is not, which occurs at \( \theta = \frac{\pi}{2} \). Therefore, within the given range \( -\frac{\pi}{2} < \theta \leq \frac{\pi}{2} \), the only solution is: \[ \theta = \frac{\pi}{2} \] The cotangent function, \( \cot(\theta) \), is defined as the ratio of the cosine to the sine: \( \cot(\theta) = \frac{\cos(\theta)}{\sin(\theta)} \). At \( \theta = \frac{\pi}{2} \), the cosine value is indeed zero while the sine value is one, confirming that \( \cot(\frac{\pi}{2}) = 0 \).