[tex]\bf tan(\theta)=2sin(\theta)\qquad
\begin{cases}
tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\qquad thus
\end{cases}\\\\
-----------------------------\\\\
\cfrac{sin(\theta)}{cos(\theta)}=2sin(\theta)\implies \cfrac{sin(\theta)}{2sin(\theta)}=cos(\theta)\implies \cfrac{1}{2}=cos(\theta)
\\\\\\
\textit{now, taking }cos^{-1}\textit{ to both sides}
\\\\
cos^{-1}\left( \cfrac{1}{2} \right)=cos^{-1}[cos(\theta)]\implies cos^{-1}\left( \cfrac{1}{2} \right)=\measuredangle \theta[/tex]
