[tex]\bf sin\left[ tan^{-1}(0) \right]\textit{ now, if }tan^{-1}(0)=\theta \textit{ that simply means }tan(\theta )=0
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tan(\theta)=\cfrac{sin(\theta)}{cos(\theta)}\impliedby
\begin{array}{llll}
\textit{because of that, tangent is only 0}\\
\textit{when sine is 0}
\end{array}
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\textit{and sine is 0 only at }\quad \boxed{0,\pi ,2\pi} \textit{ on the interval of }[0,2\pi ][/tex]
