Trig identity please help!

cot^2(x) - cot^2 (y) = [cos^2(x) - cos^2(y)] / [sin^2(x)•sin^2(y)]

thanks in advance! please prove!
and show all steps

.............cos Θ
cot Θ =▬▬▬
.............sin Θ

so

cot² x - cot² y

=

cos² xsin²y............sin² x..cos² y
▬▬▬▬▬▬..-..▬▬▬▬▬▬
sin² x...sin² y.........sin² x.sin² y

=

cos² x(1-cos²y)...▬..(1-.cos² x)..cos² y
▬▬▬▬▬▬▬▬▬▬▬▬
..........sin² x.sin² y

=

................these cancel
...................↓...................…
cos² x- cos²xcos²y▬.cos²y+cos²ycos²x←
▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬
..........sin² x.sin² y

equals

cos² x..▬..cos² y
▬▬▬▬▬▬▬▬
...sin² x.sin² y