How can the lift induced drag for a wing be calculated?
Induced drag is the portion of the lift force that opposes motion.  Induced drag exists even when the drag coefficient CD in your equation is zero.

Lift is perpendicular to the air flow relative to the wing.  Imagine a wing moving right to left across your screen.  The air is moving left to right relative to the wing.  If there's no vertical induced airflow then the lift is vertical and there's no induced drag.  However, lift deflects the air down, so typically the air relative to this wing is not moving exactly left to right, but is tilted down slightly.  Hence, the lift, which is perpendicular to that airflow, is actually tilted back (right) slightly.  That means a (typically small) portion of the lift is &quot;pushing this wing back,&quot; opposing its right-to-left motion.
If you know trigonometry, induced drag is lift times the sine of the inflow angle, $ L\sin \phi $.  The inflow angle is the angle of the airflow relative to the horizontal in this picture.
There's a picture of exactly this at the bottom of this page in the induced power section.  (Induced power is the power required to overcome induced drag.)