Firstly, express the LHS in the form R sin(3θ − α).

(Note the negative sign and the 3θ! We have to increase the domain by 3 times.)

So

Now, solving the original equation gives:

Since we have 3θ , we must use the domain: 0° ≤ 3θ < 1080°.

Sine is positive in Quadrants I,II and V, VI and IX and X.

So, from calculator, we get the following for (3θ − 40.60°):

24.33°, 155.67°, 384.33°, 515.67°, 744.33° and 875.67°

So 3θ will be:

64.93°, 196.27°, 424.93°, 556.27°, 784.93°, 916.27°.

So the solutions for θ are:

21.6°, 65.4°, 141.6°, 185.4°, 261.6°, 305.4°.