Biasing in an FM transmitter circuit

An answer:

\begin{array}{rcl} I_{C} & = βfe \cdot I_{B} \\ I_{B} = \frac{V_{C} - 0.6}{R_{2}} \\ V_{C} = V_{CC} - R_{3} \cdot (I_{C} + I_{B}) \\ ⟹ \\ I_{C} & = βfe \cdot \frac{V_{CC} - R_{3} \cdot I_{C} \frac{βfe + 1}{βfe} - 0.6}{R_{2}} \\ = βfe \cdot \frac{V_{CC} - 0.6}{R_{2} + (βfe + 1) R_{3}} \\ \approx 3 mA \end{array}

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