Mathematics HW help please

Question

What are ALL the solutions of the equation cscxtanx=2√3 / 3 on the interval [0,2π)?

answer options:

5pi/3

pi/6

4pi/3

pi/4

pi/3

pi

pi/2

2pi/3

3pi/4

5pi/6

7pi/6

5pi/4

3pi/2

7pi/4

11pi/6



Answer 1

cscxtanx = 2sqr3/3 = 2/sqr3

cscxtanx = (1/sinx)(sinx/cosx) = 1/cosx = secx

cosx = sqr3/2

x = cos^-1(sqr3/2) = 30 or 330 degrees = pi/6 or 11pi/6

among the answer options: 2nd and last