Verified answer

tan (3θ-4°)=1/cot (5θ-8°)

⇒ tan (3θ-4°)=tan (5θ-8°) [Note that tan θ = 1/cot θ]

⇒ 3θ-4° = 5θ-8°

⇒ 2θ = 4°

⇒ θ = 2°

you know that the ti 89 has an "solver" you plug in the equation and it finds the missing variable for you....