Given: θ₁, θ₂, θ₃,…, θ_n is A.P

∴ θ₂ – θ₁ = θ₃ – θ₂ = θ₄ – θ₃ =…………= θ_n – θ_n-1 = d (Common Difference)

Now,

Multiplying and dividing by sin d:

{∵ sin(A - B) = sin A cos B - cos A sin B}

Similarly,

Take L.H.S.:

Putting the value of (i), (ii) and (iii):

= R.H.S.

Hence Proved