calculus - What is the integration of integral of $cot(log(sin(x))$ ??

what is the integration of integral
$$\int\cot(\log(\sin(x))\, dx$$

I have tried:

Let $\log(\sin(x))=z$ or $\dfrac{1}{\sin(x)}\cos(x)\cdot dx=dz$ , that means $\cot(x)\cdot dx=dz$ $\Longrightarrow$ integration of $dz$ is $z$ then $c=\dfrac{\log(\sin(x))^2}{2}c$ is it true?