Condition for Valid Time Indication

Theorem
Consider an analogue clock $C$ with an hour hand $H$ and a minute hand $M$.

Let the angle made by the minute hand with respect to the twelve o'clock position be $\theta$.

Let the angle made by the hour hand with respect to the twelve o'clock position be $\phi$.

Then $C$ displays a valid time indication :


 * $12 \phi \mod 30 = \theta$