Trigonometry

Trignometry is helpful in triangle based mathematical analysis. One of various trigonometric relation is tan (A+B) $$= \frac{tan  A  +  tan B}{1- tan  A  tan  B}$$.
Now consider a diagram representing a triangular roof frame ABC with a window frame EFC. BC and EF are horizontal and AD and FC are vertical.
If $$\dfrac {\sin^{3}\theta+\cos^{3}\theta}{\sin \theta+\cos \theta}+\dfrac {\sin^{3}\theta-\cos^{3}\theta}{\sin \theta-\cos \theta}=K$$,  then K =
If $$7 (\theta) = (2n + 1)\pi$$, when $$n = 0, 1, 2, 3, 4, 5, 6,$$ then
On the basis of above information, answer the following questions:
If $$\tan A=\sqrt{3}$$, then verify that $$\sin^{2}A+\cos^{2}A=1$$.
State if the given angles are conterminal.
$$\alpha =185^{\circ}, \beta =-545^{\circ}$$