[tex]\bf \textit{Sum and Difference Identities}
\\ \quad \\
sin({{ \alpha}} + {{ \beta}})=sin({{ \alpha}})cos({{ \beta}}) + cos({{ \alpha}})sin({{ \beta}})
\\ \quad \\
sin({{ \alpha}} - {{ \beta}})=sin({{ \alpha}})cos({{ \beta}})- cos({{ \alpha}})sin({{ \beta}})\\\\
-------------------------------\\\\
sin(\theta )cos(3\theta )+cos(\theta )sin(3\theta )=0\implies sin(\theta ~+~3\theta )=0[/tex]
[tex]\bf sin(4\theta )=0\implies 4\theta =sin^{-1}(0)\implies 4\theta =
\begin{cases}
0\\
\pi \\
2\pi
\end{cases}\\\\
-------------------------------\\\\
4\theta =0\implies \measuredangle \theta =0\\\\
-------------------------------\\\\
4\theta =\pi \implies \measuredangle \theta =\cfrac{\pi }{4}\\\\
-------------------------------\\\\
4\theta =2\pi \implies \measuredangle \theta =\cfrac{2\pi }{4}\implies \measuredangle \theta =\cfrac{\pi }{2}
[/tex]
