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The figure shows the single line diagram of a single machine infinite bus system.

The inertia constant of the synchronous generator $H = 5 \: MW-s/MVA$. Frequency is $50 \: Hz$. Mechanical power is $1 \: pu$. The system is operating at the stable equilibrium point with rotor angle equal to $30^{\circ}$. A three phase short circuit fault occurs at a certain location on one of the circuits of the double circuit transmission line. During fault, electrical power in $pu$ is $P_{max} \sin\delta$ . If the values of $\delta$ and $d\delta / dt$ at the instant of fault clearing are $45^{\circ}$ and $3.762 \text{ radian/s}$ respectively, then $P_{\text{max}}$ (in $pu$) is _______.

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