Exterior angle equals the sum of two non-adjacent interior angles

Dependencies: Triangle interior angles sum to 180°, Linear pair sums to 180°.

Statement

Let $\triangle ABC$ have side $BC$ extended along its original direction to a point $D$ (so that $C$ lies between $B$ and $D$). Call $\angle ACD$ the exterior angle of $\triangle ABC$ at vertex $C$, denoted $\gamma'$. Then