The simplified form of tan−1⁡3a2x−x3a3−3ax2, a>0;−a3≤x≤a3 is

Let x = a tan θ⇒    xa=tan⁡θ⇒   θ=tan−1⁡xa∴tan−1⁡3a2x−x3a3−3ax2=tan−1⁡3a2(atan⁡θ)−(atan⁡θ)3a3−3a(atan⁡θ)2 =tan−1⁡a33tan⁡θ−tan3⁡θa31−3tan2⁡θ=tan−1⁡3tan⁡θ−tan3⁡θ1−3tan2⁡θ=tan−1⁡(tan⁡3θ)=3θ=3tan−1⁡xa     [from Eq. (i)]