If tan⁡β=2sin⁡αsin⁡γcosec⁡(α+γ) then cot⁡α,cot⁡β,cot⁡γ are in

tan⁡β=2sin⁡αsin⁡γcosec⁡(α+γ)=2sin⁡αsin⁡γsin⁡(α+γ)or  cot⁡β=sin⁡(α+γ)2sin⁡αsin⁡γor 2cot⁡β=sin⁡αcos⁡γ+cos⁡αsin⁡γsin⁡αsin⁡γ=cot⁡α+cot⁡γ or cot⁡α,cot⁡β,cot⁡γ are in A.P.