For the following open$-$loop transfer function:

$G(s)=\frac{4e^{-0\mathrm{.}1s}}{s^2+s+1}$

a$.$ Find the phase margin.

b$.$ Can the delay be reduced enough to obtain a phase margin of $45?$ If yes, find the required delay. If not, find a combination of loop gain and delay that produces a phase margin of $45.$