If the inverse trigonometric functions take principal values then

$${\cos ^{ - 1}}\left( {{3 \over {10}}\cos \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right) + {2 \over 5}\sin \left( {{{\tan }^{ - 1}}\left( {{4 \over 3}} \right)} \right)} \right)$$ is equal to :

Let f : R $$\to$$ R satisfy $$f(x + y) = {2^x}f(y) + {4^y}f(x)$$, $$\forall$$x, y $$\in$$ R. If f(2) = 3, then $$14.\,{{f'(4)} \over {f'(2)}}$$ is equal to ____________.

Let p and q be two real numbers such that p + q = 3 and p⁴ + q⁴ = 369. Then $${\left( {{1 \over p} + {1 \over q}} \right)^{ - 2}}$$ is equal to _________.

If $${z^2} + z + 1 = 0$$, $$z \in C$$, then

$$\left| {\sum\limits_{n = 1}^{15} {{{\left( {{z^n} + {{( - 1)}^n}{1 \over {{z^n}}}} \right)}^2}} } \right|$$ is equal to _________.