Evaluate the following $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $$

There exists a value of $$\theta $$ between 0 and $$2\pi $$ that satisfies the equation $$\,\,{\sin ^4}\theta - 2{\sin ^2}\theta - 1 = 0.$$

$$\left( {1 + \cos {\pi \over 8}} \right)\left( {1 + \cos {{3\pi } \over 8}} \right)\left( {1 + \cos {{5\pi } \over 8}} \right)\left( {1 + \cos {{7\pi } \over 8}} \right)$$ is equal to

If 1, $${{a_1}}$$, $${{a_2}}$$......,$${a_{n - 1}}$$ are the n roots of unity, then show that (1- $${{a_1}}$$) (1- $${{a_2}}$$) (1- $${{a_3}}$$) ....$$(1 - \,a{ - _{n - 1}}) = n$$