= Solution
The intercept is the midpoint of the two <log odds>:
$$
\boxed{\alpha=\tfrac12[\operatorname{logit}\theta_C+\operatorname{logit}\theta_T].}
$$
Equivalently $e^\alpha$ is the geometric mean of the two odds. The <logistic function> evaluated at $\alpha$ represents a central event probability, and approximates the average of the two group probabilities when $\beta$ is small. \b[It is not generally their arithmetic average], nor is $\alpha$ specifically the control-group <log odds>.
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