Help - A beam of spin-1 particles is sent through a series of three Stern-Gerlach measuring devices

I've been working on this problem for several hours and have no idea what to do. Any help would be much appreciated.

A beam of spin-1 particles is sent through a series of three Stern-Gerlach measuring devices (Fig. 3.11). The first SGz device transmits particles with Sz = hbar and filters out particles with Sz = 0 and -hbar. The second device, an SGn device, transmits particles with Sn = hbar and filters out particles with Sn = 0 and -hbar,
where the axis n makes an angle θ in the xz plane with respect to the z axis. A last SGz device transmits particles with Sz = -hbar and filters out particles with Sz = hbar and 0.

(a) What fraction of the particles transmitted by the first SGz device will survive the third measurement?
Note: The states with Sn = hbar, 0, and -hbar in the Sz basis follow directly from applying the rotation operator (see image).

(b) How must the angle θ of the SGn device be oriented so as to maximize the number of particles that are transmitted by the final SGz device? What fraction of the particles survive the third measurement of for this value of θ?

(c) What fraction of the particles survive the last measurement if the SGn device is removed from the experiment?

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