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Please please use explanation with answer

Please please use explanation with answer-example-1

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Answer:


\large\boxed{\theta=-(\pi)/(4)+k\pi\ or\ \theta=k\pi}\ for\ k\in\mathbb{Z}

Explanation:


\tan^2\theta+\tan\theta=0\\\\\tan\theta(\tan\theta+1)=0\iff\tan\theta=0\ \vee\ \tan\theta+1=0\\\\\tan\theta=0\Rightarrow \theta=k\pi\ \text{for}\ k\in\mathbb{Z}\\\\\tan\theta+1=0\qquad\text{subtract 1 from both sides}\\\\\tan\theta=-1\Rightarrow\theta=-(\pi)/(4)+k\pi\ \text{for}\ k\in\mathbb{Z}

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