differential equations - Plotting the solutions of $y' = -frac{cos y}{sin x}$

I struggle with the problem of plotting the solution of this ODE:

$\qquad y' = -\frac{\cos y}{\sin x}$

I've already tried to use ContourPlot in a loop and in a table. For example, I tried:

For[i = 0, i < 5, i = i + 0.1,
 f5 = 

   Show[
     f5, 
     ContourPlot[y == 2*ArcTan[i/Tan[x/2]] - Pi/2, {x, -10, 10}, {y, -10, 10}]];]

In most cases I get nothing except an empty coordinate system.

I know what the curves should look like, because I worked it out by hand as shown below:

Could anybody point to possible way of plotting this "leafs"? Thank you!

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