Obtaining P(w) expression from figure for zero ISI
The P(w) function (if my assumption is correct from the statement) is a pure-real trapezoid function.  The Nyquist filter(f)/waveform(t) function pair also gives that the F(w) be doubly symmetric about 2*pi()/T.

Therefore, in this example, the doubly symmetric point (in w) is (w1 + w2)/2  So T = 1/(pi() * (w1 + w2)).  Doubly symmetric in w means that from some mid-amplitude point, moving left from the symmetry point gives the even-rotated image of what is to the right of the symmetry point for a left-side and a right-side (doubly) transition band midpoint.

Now to the question at hand, the trapezoid in w can be looked up in a transform pair handbook.  It will have a sinc() term (due to the flat top portion) and sinc^2 term (due to the ramping sides) and you will find that it has a value of 1 at 0 and 0 at integer multiples of T.  You can also approach it as a pair of inverted &amp; scaled triangle functions ... shaped like ^  ... one smaller than the other, that exactly cancel across the middle section to make it flat.