If `"c o s e c"^(-1)x+"c o s e c"^(-1)y+"c o s e c"^(-1)z=-(3pi)/2` , find the value of `x/y+y/z+z/x` .

Explanation

`cosec^(-1)x+cosec^(-1)y+cosec^(-1)z=-(3pi)/2`

`cosec^(-1)x=(-pi/2), cosec^(-1)y=(-pi/2), cosec^(-1)z=(-pi/2)`

`x=-1, y=-1, z=-1`


` x/y+y/z+z/x=3`