Graze me, Hit me

There are two parallel planes, each inclined to the horizontal at an angle $\theta$ . A particle is projected from a point midway between the foot of the two planes so that it grazes one of the planes and strikes the other at a right angle. Find the angle of projection of the projectile.

If this angle can be expressed as $\tan^{-1} (a \cot \theta) + \theta$ , submit your answer as $a^2 + 2\sqrt2$ .

Note : Diagram is not necessarily up to scale.