If ${\cos }^2\theta +2{\sin }^2\theta +3{\cos }^2\theta +4{\sin }^2\theta +\mathrm{......10}\text{\hspace{0.17em}terms}=30$, where $0<\theta <180°$, then the value of $\cos \theta -\sin \theta$ is

$\begin{array}{l}Ifco{s}^2\theta +2{\sin }^2\theta +3{\cos }^2\theta +4{\sin }^2\theta +\mathrm{.....}=30\\ {\cos }^2\theta (1+3+5+7+9)+{\sin }^2\theta (2+4+6+8+10)=30\\ 25{\cos }^2\theta +30{\sin }^2\theta =30\\ 25{\cos }^2\theta +25{\sin }^2\theta +5{\sin }^2\theta =30\\ 25+5{\sin }^2\theta =30\\ 5{\sin }^2\theta =5\\ {\sin }^2\theta =1\\ \theta =90°[\because 0<\theta <180°]\\ \therefore \cos \theta -\sin \theta =\cos 90°-\sin 90°\\ =-1\end{array}$