(1)4sin theta - 3csc theta = 0 --> 4 sin x - 3 csc x = 0;

4 sin x - 3(1/sin x) = 0,

(4 sin^2 x - 3)/sin x = 0,

4 sin^2 x - 3 = 0,

4 sin^2 x = 3,

sin^2 x - 3/4 = 0, factoring it.

(sin x + (sqrt 3)/2)(sin x - (sqrt 3)/2) = 0, the roots are

sin x = (sqrt 3)/2, -(sqrt 3)/2.

x = arcsin ((sqrt 3)/2, -(sqrt 3)/2)

x = {60, 120, 240, 300 degrees} or {pi/3, 2pi/3, 4pi/3, 5pi/3}