A precision robotic arm is calibrated such that its angular deviation ψ\psiψ (in degrees) from a reference plane satisfies the equilibrium alignment condition:
3tan(ψ+60∘)=5cos(ψ+60∘)3 \tan(\psi + 60^\circ) = 5 \cos(\psi + 60^\circ)3tan(ψ+60∘)=5cos(ψ+60∘)
Solve this equation for the interval −180∘<ψ≤180∘-180^\circ < \psi \le 180^\circ−180∘<ψ≤180∘.
Give your answers to one decimal place where appropriate.