Sin 3θ= cos(θ-26) Solve for θ

I think you will need to solve this numerically.  The graphs below might help:

The first two solutions above are at θ = 29° and 32°

On second thoughts, a numerical solution might be overkill!  If θ - 26° is in the first quadrant, then cos(θ - 26°) = sin(90°- θ + 26°).  In this case 3θ = 116° - θ or 4θ = 116° or θ = 29°.

Yes I'll go for Alan's second answer,

Consider this triangle,          $$sin\theta = \frac{o}{hyp} = cos(90-\theta)$$

so in your question

$$\\sin3\theta = cos(90-3\theta)=cos(\theta-26)\\ therefore\\ 90-3\theta=\theta-26\\ 116=4\theta\\ \theta=29^0$$