• where not met in 200 iterations

If tan⁡α=−12\displaystyle {\tan{\alpha}}=-\frac{{1}}{{2}} such that α\displaystyle \alpha terminates in quadrant II and cot⁡β=−2\displaystyle {\cot{\beta}}=-{2} such that β\displaystyle \beta terminates in quadrant IV then

 sin⁡(α−β)=\displaystyle {\sin{{\left(\alpha-\beta\right)}}}=  

Your answer should be exact but you do not have to rationalize your denominator.

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