Prove that tan^3 theta-1 by tan theta-1=sec^2 theta+tan theta?

(Tan^3θ-1)/Tanθ =Sec^2θ+Tanθ

R.H.S=Sec^2θ+Tanθ
=(1/Cos^2θ) + (Sinθ/Cosθ)
=(1+Cosθ.Sinθ)/Cos^2θ
=(1/Cos^2θ) + (Cosθ.Sinθ)/Cos^2θ
=Sec^2θ+(Sinθ/Cosθ)
=Sec^2θ+Tanθ

Hence Proved