Where exactly are you having problems? A precise statement of what the model is would be useful - it isn't clear to me where the blocks are showing up, given the way the question is phrased.

The anticipation is that the orthogonality is going to cause the contrasts to be uncorrelated. If is the BLUE of and and are orthogonal contrasts, you are going to want to see what happens when you calculate

.

If is proportional to the identity matrix, this is going to give you everything immediately.