In a ∆ABC, if tan A : tan B : tan c = 3 : 4: 5, then the value of sin A . sin B . sin C is equal to

Let tan A =3k, tan B = 4k and tan C = 5k intriangle ABC,A+B+C=180tan A+ tan B + tan C= tan A tan B tan C, ⇒ 12k=60k3⇒ k=15∴ tan⁡A=35,tan⁡B=45∴ sin⁡A=314,sin⁡B=421,sin⁡C=56Hence sin⁡A⋅sin⁡B⋅sin⁡C=257