If, \[\large p^{2}=a^{2}cos^{2}\theta+b^{2}sin^{2}\theta\] then the value of \[\large p+\frac{d^{2}p}{d\theta^{2}}\] can be represented as - \[\large \frac{a^{x}b^{y}}{p^{z}}\] Where \(\large x,y,z\) are positive integers and need not to be distinct.

Then find the value of \(\large x+y+z\).

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