cos³x.csc³x = 4cot²x
cos³x.(1/sin³x) = 4cot²x
cot³x = 4cot²x
cot³x - 4cot²x = 0
cot²x(cotx - 4) = 0
Roots then are: cotx = 0, cotx = 4, i.e.
x = pi/2, x = atan(1/4)
For solutions in the range [0..360],
Answer: x = pi/2, x = 3pi/2, x = atan(1/4), x = atan(1/4) + pi