Mathematics - Point Question with Solution | TestHub

A line passing through the point $\mathrm{P}(\mathrm{a},\theta )$ makes an acute angle $\alpha$ with the positive x -axis. Let this line be rotated about the point $P$ through an angle $\frac{\alpha }{2}$ in the clock-wise direction. If in the new position, the slope of the line is $2-\sqrt{3}$ and its distance from the origin is $\frac{1}{\sqrt{2}}$, then the value of $3a^2{\tan }^2\alpha -2\sqrt{3}$ is