Recall the Pythagorean identity,
[tex]\sec^2\theta=1+\tan^2\theta[/tex]
So we have
[tex]\sec^2\theta=4+2\tan^2\theta[/tex]
[tex]1+\tan^2\theta=4+2\tan^2\theta[/tex]
[tex]-3=\tan^2\theta[/tex]
But squaring any real number always gives a non-negative number, so there are no real solutions to this equation.
