Help With A level Trig

how do I find the values of theta for the equation: sin(60∘+θ)=cosθ
for 0∘≤θ≤360∘

Edit: I have got the lowest value which is 15, I am just unsure on how to work out the 2nd value

You could use the complementary identity for sin or cos.

I used cos theta = sin (90 - theta)
I am unsure how to calculate the other value using it though

Thats what I meant. So when you do arcsin, what are the multiple values? If necessary, think of cast or sin curves.

When I done it I done:
sin(60+theta) = sin(90-theta)
60+theta = 90-theta
Then solved to get theta = 15

How do I do the arcsin in this case?

When you go from line 1 to line 2 (bold) you take inverse sin or arcsin. sin has a restricted domain to make it invertible so when you do the inverse its got multiple solutions. As an example
sin(x) = sin(90-x)
is obviously satisfied by x=45 so sin(x) = 1/sqrt(2) but also by x=225
https://www.desmos.com/calculator/bybfbtk8ci
when sin(x)=-1/sqrt(x).

arcsin is has a range -90 to 90 and you have to explcitly think about solutions outside that domain.

Thank you I have got the right answer now. I had to add 180 each time, which makes sense now I look at the ATSC diagram