Let M and N be foots of the perpendiculars drawn from the point $\mathrm{P}(\mathrm{a}, \mathrm{a}, \mathrm{a})$ on the lines $x-y=0, \mathrm{z}=1$ and $x+y=0, \mathrm{z}=-1$ respectively and if $\angle \mathrm{MPN}=90^{\circ}$ then $\mathrm{a}^2=$

If $\theta$ is the angle between the lines whose direction cosines are given by $6 \mathrm{mn}-2 \mathrm{n} l+5 l \mathrm{~m}=0$ and $3 l+\mathrm{m}+5 \mathrm{n}=0$, then $\sin \theta=$