Answer question and show work please?

Question

solve the equation foe the interval [0, 2pie]

csc^5x - 4cscx = 0

Answer 1

csc⁵x - 4cscx = 0 [0, 2pi]

Take out common term cscx

cscx(csc⁴x - 4) = 0

cscx = 0 or csc⁴x - 4 = 0

sinx = ∞ This is wrong

Therefore csc⁴x = 4

Take fourth root  to each side

cscx = ±√2 at  [0 , 2pi]

sinx = ±(1 / √2)  at [0 , 2pi]

x = pi / 4 , 3pi / 4 , 5pi / 4 , 7pi / 4.