Let me floor

If $\left\lfloor\frac {\pi}{2} + \frac {2}{3} \left (1-\frac {\pi e^{\pi}}{e^{\pi}-1+100\cos\left( \frac \pi {\sqrt 3} \right)}\right)\right\rfloor=a^a$ Find the value of $a^a +a$ .

Notation: $\left\lfloor \cdot \right\rfloor$ denotes the floor function .

Inspired by Sir Srinivasa Raghava's problem which is still an open problem and this one too.