[tex]\bf \textit{triple angle identities}\\\\
sin(3\theta )=3sin(\theta )-4sin^3(\theta )\\\\
-------------------------------[/tex]
[tex]\bf \begin{array}{llll}
3sin(\theta )&-2sin^3(\theta )&-2sin^3(\theta )\\\\
&-2\underline{sin^2(\theta )} sin(\theta )\\\\
&-2[\underline{1-cos^2(\theta )}]sin(\theta )\\\\
&[-2+2cos^2(\theta )]sin(\theta )\\\\
&-2sin(\theta )+2cos^2(\theta )sin(\theta )
\end{array}
\\\\\\
3sin(\theta )\boxed{-2sin(\theta )+2cos^2(\theta )sin(\theta )}-2sin^3(\theta )
\\\\\\
sin(\theta )+2cos^2(\theta )sin(\theta )-2sin^3(\theta )
\\\\\\
2cos^2(\theta )sin(\theta )+sin(\theta )-2sin^3(\theta )[/tex]
