The value of $$\frac{sin39^{\circ}}{cos51^{\circ}}$$ + $$2 tan11^{\circ} tan31^{\circ} tan45^{\circ} tan59^{\circ} tan79^{\circ}$$ - $$3(sin^{2}21^{\circ} + sin^{2}69^{\circ})$$ is

Expression : $$\frac{sin39^{\circ}}{cos51^{\circ}}$$ + $$2 tan11^{\circ} tan31^{\circ} tan45^{\circ} tan59^{\circ} tan79^{\circ}$$ - $$3(sin^{2}21^{\circ} + sin^{2}69^{\circ})$$

= $$\frac{sin 39^{\circ}}{cos (90^{\circ} - 39^{\circ})}$$ + $$2 \times tan 11^{\circ} \times tan 31^{\circ}$$ $$\times 1 \times tan (90^{\circ} - 31^{\circ}) \times tan (90^{\circ} - 11^{\circ})$$ - $$3 [sin^2 21^{\circ} + cos^2 (90^{\circ} - 21^{\circ})]$$

= $$\frac{sin 39^{\circ}}{sin 39^{\circ}}$$ + $$2 \times tan 11^{\circ} \times cot 11^{\circ} \times tan 31^{\circ} \times cot 31^{\circ}$$ - $$3(sin^2 21^{\circ} + cos^2 21^{\circ})$$

= $$1 + 2 - 3 = 0$$