Solving $\sin\theta -1=\cos\theta $ 
Solve$$\sin\theta -1=\cos\theta $$

Steps I took to solve this:
$$\sin^{ 2 }\theta -2\sin\theta +1=1-\sin^2\theta $$
$$2\sin^{ 2 }\theta -2\sin\theta =0$$
$$(2\sin\theta )(\sin\theta -1)=0$$
$$2\sin\theta =0, \sin\theta -1=0$$ 
$$\quad \sin\theta =0, \sin\theta =1$$
$$\theta =0+\pi k, \theta =\frac { \pi  }{ 2 } +2\pi k$$
Why is $\theta =0+\pi k$ wrong?

use that $$\sin(\theta)=2\,{\frac {\tan \left( \theta/2 \right) }{1+ \left( \tan \left( \theta
/2 \right)  \right) ^{2}}}
$$
and $$\cos(\theta)={\frac {1- \left( \tan \left( \theta/2 \right)  \right) ^{2}}{1+
 \left( \tan \left( \theta/2 \right)  \right) ^{2}}}
$$
