If cot⁡(θ−α),3cot⁡θ,cot⁡(θ+α) are in A.P. and θ is not an integral multiple of π2 then the value of 4sin2⁡θ3sin2⁡α=

Given cot⁡(θ−α),3cot⁡θ,cot⁡(θ+α) are in A.P⇒6cot⁡θ=cot⁡(θ−α)+cot⁡(θ+α)⇒6cos⁡θsin⁡θ=sin⁡2θsin⁡(θ+α)sin⁡(θ−α)⇒6cos⁡θsin2⁡θ−sin2⁡α=2sin2⁡θcos⁡θ⇒3sin2⁡θ−sin2⁡α=sin2⁡θ⇒2sin2⁡θ=3sin2⁡α∴2sin2⁡θ3sin2⁡α=1