The formula in the title is incomplete due to character limit, here's the full form
$$\frac{e^{i\theta_{y}}-e^{-i\theta_{y}}}{2i}\dot{\theta_{y}}^{2}$$
Into the form which has just $\dot{\theta_{y}}$ or even $\theta_{y}$(I'm not sure about the 2nd one).
As you can see the original form of the equation is from sine,$$\sin(\theta_{y})\dot{\theta_{y}}^{2}$$ written in terms of exponential.
I'm trying the product rule, and it's not that easy to think of any proper way to rewrite it or should I just use some other way to bring it down to the form where I can get the $\dot{\theta_{y}}$ or $\theta_{y}$
Is there any other rule, other than the product rule to bring it down to the form where it can be written in the form $\dot{\theta_{y}}$?