Prove that : \[ \begin{array}{r} \sin \left(40^{\circ}+\theta\right...

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Prove that :
\[
\begin{array}{r}
\sin \left(40^{\circ}+\theta\right) \cos \left(10^{\circ}+\theta\right)-\cos \left(40^{\circ}+\theta\right) \\
\sin \left(10^{\circ}+\theta\right)=\frac{1}{2}
\end{array}
\]
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