PWM to Sin 5V

Filter 0...3.3V PWM signal from BeagleBone Black to a 60Hz, 0...5V sinusoidal signal. First stage filters to ~60Hz. Second stage brings it down to +/- 2.5V. Third stage shifts it back up to 0...5V. The reason for bringing it down to +/- 2.5V is so that when I decrease the PWM duty cycle, the signal shrinks towards 2.5V rather than 0V. If this functionality is not needed, then a simple single stage amplifier may be a better choice.