Trigonometry

$$\frac{{\sin \,\theta \, - \,2\,{{\sin }^3}\,\theta }}{{2\,{{\cos }^3}\theta \, - \,\cos \,\theta }}\, = \,\tan \,\theta $$
The value of $$\sin ( 360^o - \theta)  $$ is
From the following figure,
From the top of a building, $$60$$ metres high, the angles of depression of the top and bottom of a vertical lamp-post are observed to be $${30}^{o}$$ and $${60}^{o}$$ respectively. Find:
The value of $$\sin { \left( {{ 45 }}^{o} +\theta  \right)  } -\cos { \left( {{ 45 }}^{o} -\theta  \right)  } $$ is