The angular deflection θ\thetaθ of a precision tracking gimbal is governed by the equilibrium condition
4sinθcosθ2sinθ+3=tanθ,sinθ≠−32 \frac{4 \sin \theta \cos \theta}{2 \sin \theta + 3} = \tan \theta, \quad \sin \theta \neq -\frac{3}{2} 2sinθ+34sinθcosθ=tanθ,sinθ=−23Show that this equation can be written in the form
4sin3θ+2sin2θ−sinθ=0 4\sin^3\theta + 2\sin^2\theta - \sin\theta = 0 4sin3θ+2sin2θ−sinθ=0Determine the possible values for the angular deflection xxx of the gimbal in the range −π2<x<π2-\frac{\pi}{2} < x < \frac{\pi}{2}−2π<x<2π, giving your answers to 3 decimal places where appropriate.
