cot^2x * sinx = cot^2x

cot^2x * sinx = cot^2x    converting to sines and cosines, we have

(cos^2x / sin^2 x) * sinx  =  cos^2x/sin^2x

cos^2x/ sinx  = cos^2x/sin^2x     rearrange

cos^2x/sin^2x - cos^2x/sin^2x = 0

(cos^2x/sinx)(1/sinx - 1) = 0     setting each factor to 0 we have

cos^2x/sinx = 0        this is only = 0  where cosx = 0  = pi/2 and 3pi/2  on [0, 2pi]

And

(1/sinx - 1) = 0

cscx  -  1  = 0

cscx = 1     and this occurs at pi/2  on   [0, 2pi]

So, the solutions are (pi/2, 0) and (3pi/2, 0)

Here's the graph on [0, 2pi].....

https://www.desmos.com/calculator/ilgihnbbla