Emitter follower augmented input current
Q3 is in forward active mode because the base-emitter junction is forward biased and the base-collector junction is reverse biased.

In this mode we have the very well known characteristic 
$$I_c = \beta I_b .$$

Since the current coming out of the emitter is (by KCL) the sum of the base and collector currents, 

$$I_e = I_b + I_c = I_b + \beta I_b$$

and thus

$$I_b = \frac{I_e}{1+\beta}.$$

(Note: circuit theory purists would normally take \$I_e\$ to mean the current going in to the emitter, so there'd be some sign changes in the equations above)