If $\tan \theta ,\cot \theta$ are roots of $x^2+2ax+b=0,$then least value of $\left(a\right)$ =_____

$x^2-(\tan \theta +\cot \theta )n+\left(1\right)=0$

Compare $x^2+2ax+b=0$

$2a=-(\tan \theta +\cot \theta ),b=1$

$\frac{{\tan }^2+1}{\tan \theta }+2a=0$

${\tan }^2\theta +1+2a\tan \theta =0$

Least value of $a=1$