Can anyone help me with C2 maths on raidans?

Find in radians correct to 2 decimal places, the two smallest positive values of θ for which sin(2θ +1/3π) = 0.123. I've worked out 2.68 but I figure out how to get to the other answer.
If you could help that would be great.

Hi, these are the steps I used:
(I'll have to use 'a' for theta as I cannot get that symbol)

sin(2a+1/3pi)=0.123
2a+1/3pi=sin^-1(0.123)
2a+1/3pi=0.123
2a=-0.925
a=-0.462

You then use the symmetry of the sin(a) graph:
(-pi)+0.462= -2.68

I hope two things: that's correct and that it helps you if it is. I cannot see how you got +2.68 (unless there is a typo in the original message or my working out)

It asks for positive values.

If you call $x = 2\theta + \frac{\pi}{3}$ and then solve $\sin x = 0.123$ then we have $x=\sin^{-1} 0.123 + 2\pi$ and then $x = \pi - \sin^{-1} (0.123) +2\pi$.

Back-sub: $2\theta+ \frac{\pi}{3} = \sin^{-1} 0.123 + 2\pi$ (solve for theta) for the first solution and $2\theta + \frac{\pi}{3} = \pi - \sin^{-1} (0.123) +2\pi$ for the second solution.

Ok I can solve it but how did you get 2Pi? Other than that, thanks for help.

Ok. Yeah that makes sense thanks.

No problem.

Hi, did u ever get 0.99 as a value, bcoz that's the other answer in the back of my textbook? I can't get that answer. It may be wrong.