If $\sin \alpha +\cos \alpha =1.2$, then what is $\sin^3\alpha + \cos^3\alpha$? If $\sin \alpha +\cos \alpha =1.2$, then what is $\sin^3\alpha + \cos^3\alpha$?

All I know is that $\sin^{3}a+\cos^{3}a$ is equal to 
$$(\sin a + \cos a)(\sin^{2} a - \sin a \cos a + \cos^{2} a)= \dfrac{6}{5}(\sin^{2} a - \sin a \cos a + \cos^{2} a)$$  But now, I'm stuck.  Solutions are greatly appreciated.

Hint:$$\left( \sin  a+\cos  a \right) \left( \sin ^{ 2 } a-\sin  a\cos  a+\cos ^{ 2 } a \right) =\\ =\left( \sin  a+\cos  a \right) \left( { \left( \sin  a+\cos  a \right)  }^{ 2 }-\frac { 3 }{ 2 } \left( { \left( \sin { a } +\cos { a }  \right)  }^{ 2 }-1 \right)  \right)  $$
