If cos−1⁡p+cos−1⁡1−p+cos−1⁡1−q=3π2, then the value of q is

Let α=cos−1⁡p,β=cos−1⁡1−pand γ=cos−1⁡1−q or cos⁡α=p,cos⁡β=1−pand cos⁡γ=1−qTherefore, sin⁡α=1−p,sin⁡β=p,sin⁡γ=qThe given equation may be written as α+β+γ=3π4or α+β=3π4−γ or cos⁡(α+β)=cos⁡3π4−γ⇒cos⁡αcos⁡β−sin⁡γsin⁡β=cos⁡[π−(π/4+γ)]=−cos⁡π4+γ⇒p1−p−1−pp=−121−q−12q ⇒0=1−q−q⇒1−q=q⇒q=12