By regrouping the LHS and multiplying and dividing by 4 we get,

But 2sin A sin B = cos (A–B) –cos (A+B)

Then the above equation becomes,

But cos(90°–θ)=sin θ and cos(180°–θ)=–cos(θ).

Then the above equation becomes,

Now,

Substituting the corresponding values, we get

Hence proved