The value of tan−1⁡(tan⁡(−6)),is

We know that tan−1⁡(tan⁡θ)=θ, if −π2<θ<π2Here, θ=−6 radians which does not lie between −π2 and π2However 2π-6 lies between −π2 and π2 such that    tan⁡(2π−6)=−tan⁡6=tan⁡(−6)∴     tan−1⁡{tan⁡(−6)}=tan−1⁡{tan⁡(2π−6)}=2π−6