find all solutions of the given Equation 48 csc2 theta 36 0

find all solutions of the given Equation

[48/ csc^2 (theta)] -36 = 0

Please show me the work step by step. i prefer hand written

Solution

48/csc^2 theta-36=0

48/csc^2theta=36

csc^2 theta= 48/36=4/3

csc theta= +-2/sqrt3

Taking inverse on both sides

theta=csc^-1(+-2/sqrt3)

theta= pi* k   - 4pi/3 , pi*k - 2pi/3