If $A+B+C=π$, verify the given If $A+B+C=π$, prove that
$$\cos A \sin B \sin C + \cos B \sin C \sin A + \cos C \sin A \sin B=1+\cos A \cos B\cos C$$
ATTEMPT:
Here,
$$A+B+C=π$$
Now,
\begin{align*}
\text{L.H.S} &= \cos A \sin B \sin C + \cos B \sin C \sin A + \cos C \sin A \sin B \\
&=\sin C(\sin A \cos B + \cos A \sin B) + \cos C \sin A \sin B \\
&= \sin C \sin(A+B) + \sin A \sin B \cos C
\end{align*}
What should I do next?

take the trig term fro the RHs to the left and combine to get
$$
\sin C \sin(A+B) - \cos C \cos (A+B)  = -\cos (A+B+C)
$$
and now $A+B+C=\pi$...
