What is the result when soap is used in hard water?

If $\alpha$ and $\beta$ are the roots of the equation $x^2 + x + 1 = 0$ then $\alpha^{2026} + \beta^{2026} = $

The number of ways that 8 beads of different colours can be strung to form a necklace is

In $\Delta ABC$, if $\angle A = 90^\circ$, then $\sin(B - C) = $