\displaystyle[br]\begin{equation*}\sin \theta \cos \theta - \sin \theta + \cos \theta - 1 \equiv (\sin \theta +1)(\cos \theta - 1)\end{equation*}
Spoiler
\displaystyle [br]\begin{equation*}\sin \theta \cos \theta - \sin \theta + \cos \theta - 1 \equiv \sin \theta (\cos \theta -1) + (\cos \theta - 1) \equiv (\cos \theta - 1)(\sin \theta +1)\end{equation*}
\displaystyle [br]\begin{equation*}\sin \theta \cos \theta - \sin \theta + \cos \theta - 1 \equiv \sin \theta (\cos \theta -1) + (\cos \theta - 1) \equiv (\cos \theta - 1)(\sin \theta +1)\end{equation*}
\displaystyle[br]\begin{equation*}\sin \theta \cos \theta - \sin \theta + \cos \theta - 1 \equiv (\sin \theta +1)(\cos \theta - 1)\end{equation*}
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