Help /sci/

So if you measure the spin of a particle as up (+1), then rotate your equipment 180 degrees you'll get down (-1).

If you rotate it 90 degrees instead, you'll get either up or down randomly, but if you repeat the experiment enough times you get an average of 0 (up and down with equal probability).

Apparently the average value is $cos\theta$. Am I right in thinking the probability is

$P(s = 1) = \frac{cos\theta}{2} + 0.5$

Meaning if you measure a (+1) then rotate 45 degrees, the probability of getting another (+1) is 85%?