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°.