Answer
In case 1, $~~\theta_{change}~~$ is counterclockwise from $\theta = 0$
In case 2, $~~\theta_{change}~~$ is counterclockwise from $\theta = 0$
In case 3, $~~\theta_{change}~~$ is at $\theta = 0$
Work Step by Step
$\omega = \frac{d\theta}{dt}$
Then $~~\omega = 0~~$ when the slope of the $\theta$ versus $t$ curve is zero.
The rotation changes direction when the slope of the $\theta$ versus $t$ curve changes from positive to negative or from negative to positive.
In case 1, we can see that the slope of the $\theta$ versus $t$ curve changes from negative to positive when $\theta_{change} \approx 40^{\circ}$
Thus, in case 1, $~~\theta_{change}~~$ is counterclockwise from $\theta = 0$
In case 2, we can see that the slope of the $\theta$ versus $t$ curve changes from positive to negative when $\theta_{change} \approx 50^{\circ}$
Thus, in case 2, $~~\theta_{change}~~$ is counterclockwise from $\theta = 0$
In case 3, we can see that the slope of the $\theta$ versus $t$ curve changes from negative to positive when $\theta_{change} = 0$
Thus, in case 3, $~~\theta_{change}~~$ is at $\theta = 0$
