How to calculate relatedness in haplodiploid organisms (mainly full sisters and full brothers)?
It is useful to think in terms of the proportion of genetic material that an individual gets from each parent and the amount of this genetic material that will be shared with another individual (on average), and then sum this together i.e. as:

$ relatedness = prop_{mother} * shared_{mother} + prop_{father} * shared_{father} $ 

A female will share 50% of the genetic material from the mother's side and 100% if the material from the father's side with her full sisters: $0.5*0.5 + 0.5*1 = 0.75$

A female will share 50% of the genetic material from the mother's side and 0% if the material from the father's side with her brother: $0.5*0.5 + 0.5*0 = 0.25$

A male will share 50% of the genetic material from the mother's side with his sister (and doesn't get any from the father's side).

A male will share 50% of the genetic material from the mother's side with his brother (and doesn't get any from the father's side).

Remember also that this only holds if the female has only mated once.