tan−1(tan1−θ)=1−θ, when
−π2<θ<π2
θ>4−π4
θ<4−π4
4−π24<θ≤1
Clearly, 1-0 is real, if θ≤1.
tan−1(tan1−θ)=1−θ
⇒ 0≤1−θ<π2and θ≤1
⇒ 0≤1−θ<π24and θ≤1
⇒ −1≤−θ≤π24−1and θ≤1
⇒ 1−π24<θ≤1 and θ≤1⇒4−π24<θ≤1