assuming that you mean what is theta if sin 4 theta = 0 then then theta=0, 0.25pi, 0.5pi, 0.75pi...
if not then without additional information the best answer you can get is sin4theta=sin4theta
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because sin(2x) = 2sin(x)cos(x)
answer is 2.34 degrees answer is 2.34 degrees
0.75
you have to do the arcsin which is sin-1 on your calculator. i have not met anyone in my life who can do sin or arcsin in their head. not even my college teachers. your theta is equal to 20degrees
csc θ = 1/sin θ → sin θ = -1/4 cos² θ + sin² θ = 1 → cos θ = ± √(1 - sin² θ) = ± √(1 - ¼²) = ± √(1- 1/16) = ± √(15/16) = ± (√15)/4 In Quadrant III both cos and sin are negative → cos θ= -(√15)/4