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Analytic trigonometry

Question: Find all solutions of the equation

sin[theta]*(cos[theta]-1=0

My work:

sin[theta]*cos[theta]-sin[theta]

cos[theta]=0 or cos[theta]=1

*Am I going in the right path I'm really confused on what to do*

$sin({\theta})cos({\theta})=sin({\theta})$

$sin({\theta})$ is 0 if we have multiples of Pi.

${\theta}=C{\pi}$

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