Express $${1 \over {1 - \cos \,\theta + 2i\sin \theta }}$$ in the form x + iy.

If x = a + b, y = a$$\gamma $$ + b$$\beta $$ and z = a$$\beta $$ +b$$\gamma $$ where $$\gamma $$ and $$\beta $$ are the complex cube roots of unity, show that xyz = $${a^3} + {b^3}$$.